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GCSE
AQA

Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3(m + 7), multiply both m and 7 by 3, so:

3(m + 7) = 3 \times m + 3 \times 7 = 3m + 21.

Expanding brackets involves using the skills of simplifying algebra. Remember that 2 \times a = 2a and a \times a =a^2.

Example

Expand 4(3n + y).

4(3n + y) = 4 \times 3n + 4 \times y = 12n + 4y

Question

Expand k(k - 2).

k(k - 2) = k \times k - 2 \times k = k^2 - 2k

Question

Expand 3f(5 - 6f).

3f(5 - 6f) = 3f \times 5 - 3f \times 6f = 15f - 18f^2

Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, a^2 = a \times a and a^4 = a \times a \times a \times a.

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

a^2 \times a^3 = (a \times a) \times (a \times a \times a) = a^5.

Example

Expand the bracket 3b^2(2b^3 + 3b).

Multiply 3b^2 by 2b^3 first. 3 \times 2 = 6 and b^2 \times b^3 = b^5, so 3b^2 \times 2b^3 = 6b^5.

Then multiply 3b^2 by 3b. 3 \times 3 = 9 and b^2 \times b = b^3, so 3b^2 \times 3b = 9b^3.

So, 3b^2(2b^3 + 3b) = 6b^5 + 9b^3.

Question

Expand the bracket 5p^3q(4pq - 2p^5q^2 + 3p).

Multiply 5p^3q by 4pq. 5p^3q \times 4pq = 20p^4q^2.

Multiply 5p^3q by -2p^5q^2. 5p^3q \times - 2p^5q^2 = - 10p^8q^3.

Multiply 5p^3q by 3p. 5p^3q \times 3p = 15p^4q.

5p^3q(4pq - 2p^5q^2 + 3p) = 20p^4q^2 - 10p^8q^3 + 15p^4q

Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, 3(h + 2) - 4. In these cases first expand the bracket and then collect any like terms.

Example 1

Expand and simplify 3(h + 2) - 4.

3(h + 2) - 4 = 3 \times h + 3 \times 2 - 4 = 3h + 6 - 4 = 3h + 2

Example 2

Expand and simplify 6g + 2g(3g + 7).

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives: 6g + 2g(3g + 7) = 6g + 2g \times 3g + 2g \times 7 = 6g + 6g^2 + 14g

Collecting the like terms gives 6g^2 + 20g.

curriculum-key-fact
Answers are usually written with descending order of powers.

More Guides

  1. Algebraic expressions – AQA
  2. Algebraic formulae – AQA
    next
  3. Solving linear equations – AQA
    next
  4. Solving simultaneous equations – AQA
    next
  5. Solving quadratic equations – AQA
    next
  6. Inequalities – AQA
    next
  7. Sequences – AQA
    next
  8. Straight line graphs – AQA
    next
  9. Other graphs – AQA
    next
  10. Transformation of curves – Higher- AQA
    next
  11. Algebraic fractions – AQA
    next
  12. Using and interpreting graphs – AQA
    next

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Bitesize

GCSE
AQA

Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3(m + 7), multiply both m and 7 by 3, so:

3(m + 7) = 3 \times m + 3 \times 7 = 3m + 21.

Expanding brackets involves using the skills of simplifying algebra. Remember that 2 \times a = 2a and a \times a =a^2.

Example

Expand 4(3n + y).

4(3n + y) = 4 \times 3n + 4 \times y = 12n + 4y

Question

Expand k(k - 2).

k(k - 2) = k \times k - 2 \times k = k^2 - 2k

Question

Expand 3f(5 - 6f).

3f(5 - 6f) = 3f \times 5 - 3f \times 6f = 15f - 18f^2

Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, a^2 = a \times a and a^4 = a \times a \times a \times a.

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

a^2 \times a^3 = (a \times a) \times (a \times a \times a) = a^5.

Example

Expand the bracket 3b^2(2b^3 + 3b).

Multiply 3b^2 by 2b^3 first. 3 \times 2 = 6 and b^2 \times b^3 = b^5, so 3b^2 \times 2b^3 = 6b^5.

Then multiply 3b^2 by 3b. 3 \times 3 = 9 and b^2 \times b = b^3, so 3b^2 \times 3b = 9b^3.

So, 3b^2(2b^3 + 3b) = 6b^5 + 9b^3.

Question

Expand the bracket 5p^3q(4pq - 2p^5q^2 + 3p).

Multiply 5p^3q by 4pq. 5p^3q \times 4pq = 20p^4q^2.

Multiply 5p^3q by -2p^5q^2. 5p^3q \times - 2p^5q^2 = - 10p^8q^3.

Multiply 5p^3q by 3p. 5p^3q \times 3p = 15p^4q.

5p^3q(4pq - 2p^5q^2 + 3p) = 20p^4q^2 - 10p^8q^3 + 15p^4q

Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, 3(h + 2) - 4. In these cases first expand the bracket and then collect any like terms.

Example 1

Expand and simplify 3(h + 2) - 4.

3(h + 2) - 4 = 3 \times h + 3 \times 2 - 4 = 3h + 6 - 4 = 3h + 2

Example 2

Expand and simplify 6g + 2g(3g + 7).

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives: 6g + 2g(3g + 7) = 6g + 2g \times 3g + 2g \times 7 = 6g + 6g^2 + 14g

Collecting the like terms gives 6g^2 + 20g.

curriculum-key-fact
Answers are usually written with descending order of powers.

More Guides

  1. Algebraic expressions – AQA
  2. Algebraic formulae – AQA
    next
  3. Solving linear equations – AQA
    next
  4. Solving simultaneous equations – AQA
    next
  5. Solving quadratic equations – AQA
    next
  6. Inequalities – AQA
    next
  7. Sequences – AQA
    next
  8. Straight line graphs – AQA
    next
  9. Other graphs – AQA
    next
  10. Transformation of curves – Higher- AQA
    next
  11. Algebraic fractions – AQA
    next
  12. Using and interpreting graphs – AQA
    next

Struggling to get your head round revision and exams?

Our team of exam survivors will get you started and keep you going.

Meet them here

Links

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  • Bitesize KS3: Maths

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  • external-link

    Revision Buddies SUBSCRIPTION

  • external-link

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GCSE Subjects

  1. Architecture
  2. Art and Design
  3. Biology (Single Science)
  4. Business
  5. Chemistry (Single Science)
  6. Combined Science
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  8. Design and Technology
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  22. ICT
  23. Irish – Learners (CCEA)
  24. Journalism (CCEA)
  25. Learning for Life and Work (CCEA)
  26. Mandarin
  27. Maths
  28. Maths Numeracy (WJEC)
  29. Media Studies
  30. Modern Foreign Languages
  31. Moving Image Arts (CCEA)
  32. Music
  33. Physical Education
  34. Physics (Single Science)
  35. Product Design
  36. PSHE and Citizenship
  37. Religious Studies
  38. Resistant Materials
  39. Science
  40. Sociology
  41. Spanish
  42. Systems and Control
  43. Textiles
  44. Welsh Second Language (WJEC)

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Bitesize

GCSE
AQA

Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3(m + 7), multiply both m and 7 by 3, so:

3(m + 7) = 3 \times m + 3 \times 7 = 3m + 21.

Expanding brackets involves using the skills of simplifying algebra. Remember that 2 \times a = 2a and a \times a =a^2.

Example

Expand 4(3n + y).

4(3n + y) = 4 \times 3n + 4 \times y = 12n + 4y

Question

Expand k(k - 2).

k(k - 2) = k \times k - 2 \times k = k^2 - 2k

Question

Expand 3f(5 - 6f).

3f(5 - 6f) = 3f \times 5 - 3f \times 6f = 15f - 18f^2

Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, a^2 = a \times a and a^4 = a \times a \times a \times a.

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

a^2 \times a^3 = (a \times a) \times (a \times a \times a) = a^5.

Example

Expand the bracket 3b^2(2b^3 + 3b).

Multiply 3b^2 by 2b^3 first. 3 \times 2 = 6 and b^2 \times b^3 = b^5, so 3b^2 \times 2b^3 = 6b^5.

Then multiply 3b^2 by 3b. 3 \times 3 = 9 and b^2 \times b = b^3, so 3b^2 \times 3b = 9b^3.

So, 3b^2(2b^3 + 3b) = 6b^5 + 9b^3.

Question

Expand the bracket 5p^3q(4pq - 2p^5q^2 + 3p).

Multiply 5p^3q by 4pq. 5p^3q \times 4pq = 20p^4q^2.

Multiply 5p^3q by -2p^5q^2. 5p^3q \times - 2p^5q^2 = - 10p^8q^3.

Multiply 5p^3q by 3p. 5p^3q \times 3p = 15p^4q.

5p^3q(4pq - 2p^5q^2 + 3p) = 20p^4q^2 - 10p^8q^3 + 15p^4q

Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, 3(h + 2) - 4. In these cases first expand the bracket and then collect any like terms.

Example 1

Expand and simplify 3(h + 2) - 4.

3(h + 2) - 4 = 3 \times h + 3 \times 2 - 4 = 3h + 6 - 4 = 3h + 2

Example 2

Expand and simplify 6g + 2g(3g + 7).

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives: 6g + 2g(3g + 7) = 6g + 2g \times 3g + 2g \times 7 = 6g + 6g^2 + 14g

Collecting the like terms gives 6g^2 + 20g.

curriculum-key-fact
Answers are usually written with descending order of powers.

More Guides

  1. Algebraic expressions – AQA
  2. Algebraic formulae – AQA
    next
  3. Solving linear equations – AQA
    next
  4. Solving simultaneous equations – AQA
    next
  5. Solving quadratic equations – AQA
    next
  6. Inequalities – AQA
    next
  7. Sequences – AQA
    next
  8. Straight line graphs – AQA
    next
  9. Other graphs – AQA
    next
  10. Transformation of curves – Higher- AQA
    next
  11. Algebraic fractions – AQA
    next
  12. Using and interpreting graphs – AQA
    next

Struggling to get your head round revision and exams?

Our team of exam survivors will get you started and keep you going.

Meet them here

Links

Bitesize personalisation promo 2018 branding showing pie chart monitor line graph mobile

Personalise your Bitesize!

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  • Skillswise: Maths
  • Radio 4: Maths collection
  • Bitesize KS3: Maths

  • external-link

    Pearson Education

  • external-link

    Revision Buddies SUBSCRIPTION

  • external-link

    Revisio SUBSCRIPTION

  • external-link

    Seneca Learning

  • external-link

    Just Maths

GCSE Subjects

  1. Architecture
  2. Art and Design
  3. Biology (Single Science)
  4. Business
  5. Chemistry (Single Science)
  6. Combined Science
  7. Computer Science
  8. Design and Technology
  9. Digital Technology (CCEA)
  10. Drama
  11. Electronics
  12. Engineering
  13. English Language
  14. English Literature
  15. Food Technology
  16. French
  17. Geography
  18. German
  19. Graphics
  20. History
  21. Home Economics: Food and Nutrition (CCEA)
  22. ICT
  23. Irish – Learners (CCEA)
  24. Journalism (CCEA)
  25. Learning for Life and Work (CCEA)
  26. Mandarin
  27. Maths
  28. Maths Numeracy (WJEC)
  29. Media Studies
  30. Modern Foreign Languages
  31. Moving Image Arts (CCEA)
  32. Music
  33. Physical Education
  34. Physics (Single Science)
  35. Product Design
  36. PSHE and Citizenship
  37. Religious Studies
  38. Resistant Materials
  39. Science
  40. Sociology
  41. Spanish
  42. Systems and Control
  43. Textiles
  44. Welsh Second Language (WJEC)

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Bitesize

GCSE
AQA

Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3(m + 7), multiply both m and 7 by 3, so:

3(m + 7) = 3 \times m + 3 \times 7 = 3m + 21.

Expanding brackets involves using the skills of simplifying algebra. Remember that 2 \times a = 2a and a \times a =a^2.

Example

Expand 4(3n + y).

4(3n + y) = 4 \times 3n + 4 \times y = 12n + 4y

Question

Expand k(k - 2).

k(k - 2) = k \times k - 2 \times k = k^2 - 2k

Question

Expand 3f(5 - 6f).

3f(5 - 6f) = 3f \times 5 - 3f \times 6f = 15f - 18f^2

Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, a^2 = a \times a and a^4 = a \times a \times a \times a.

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

a^2 \times a^3 = (a \times a) \times (a \times a \times a) = a^5.

Example

Expand the bracket 3b^2(2b^3 + 3b).

Multiply 3b^2 by 2b^3 first. 3 \times 2 = 6 and b^2 \times b^3 = b^5, so 3b^2 \times 2b^3 = 6b^5.

Then multiply 3b^2 by 3b. 3 \times 3 = 9 and b^2 \times b = b^3, so 3b^2 \times 3b = 9b^3.

So, 3b^2(2b^3 + 3b) = 6b^5 + 9b^3.

Question

Expand the bracket 5p^3q(4pq - 2p^5q^2 + 3p).

Multiply 5p^3q by 4pq. 5p^3q \times 4pq = 20p^4q^2.

Multiply 5p^3q by -2p^5q^2. 5p^3q \times - 2p^5q^2 = - 10p^8q^3.

Multiply 5p^3q by 3p. 5p^3q \times 3p = 15p^4q.

5p^3q(4pq - 2p^5q^2 + 3p) = 20p^4q^2 - 10p^8q^3 + 15p^4q

Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, 3(h + 2) - 4. In these cases first expand the bracket and then collect any like terms.

Example 1

Expand and simplify 3(h + 2) - 4.

3(h + 2) - 4 = 3 \times h + 3 \times 2 - 4 = 3h + 6 - 4 = 3h + 2

Example 2

Expand and simplify 6g + 2g(3g + 7).

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives: 6g + 2g(3g + 7) = 6g + 2g \times 3g + 2g \times 7 = 6g + 6g^2 + 14g

Collecting the like terms gives 6g^2 + 20g.

curriculum-key-fact
Answers are usually written with descending order of powers.

More Guides

  1. Algebraic expressions – AQA
  2. Algebraic formulae – AQA
    next
  3. Solving linear equations – AQA
    next
  4. Solving simultaneous equations – AQA
    next
  5. Solving quadratic equations – AQA
    next
  6. Inequalities – AQA
    next
  7. Sequences – AQA
    next
  8. Straight line graphs – AQA
    next
  9. Other graphs – AQA
    next
  10. Transformation of curves – Higher- AQA
    next
  11. Algebraic fractions – AQA
    next
  12. Using and interpreting graphs – AQA
    next

Struggling to get your head round revision and exams?

Our team of exam survivors will get you started and keep you going.

Meet them here

Links

Bitesize personalisation promo 2018 branding showing pie chart monitor line graph mobile

Personalise your Bitesize!

Sign in, choose your GCSE subjects and see content that's tailored for you.

  • Skillswise: Maths
  • Radio 4: Maths collection
  • Bitesize KS3: Maths

  • external-link

    Pearson Education

  • external-link

    Revision Buddies SUBSCRIPTION

  • external-link

    Revisio SUBSCRIPTION

  • external-link

    Seneca Learning

  • external-link

    Just Maths

GCSE Subjects

  1. Architecture
  2. Art and Design
  3. Biology (Single Science)
  4. Business
  5. Chemistry (Single Science)
  6. Combined Science
  7. Computer Science
  8. Design and Technology
  9. Digital Technology (CCEA)
  10. Drama
  11. Electronics
  12. Engineering
  13. English Language
  14. English Literature
  15. Food Technology
  16. French
  17. Geography
  18. German
  19. Graphics
  20. History
  21. Home Economics: Food and Nutrition (CCEA)
  22. ICT
  23. Irish – Learners (CCEA)
  24. Journalism (CCEA)
  25. Learning for Life and Work (CCEA)
  26. Mandarin
  27. Maths
  28. Maths Numeracy (WJEC)
  29. Media Studies
  30. Modern Foreign Languages
  31. Moving Image Arts (CCEA)
  32. Music
  33. Physical Education
  34. Physics (Single Science)
  35. Product Design
  36. PSHE and Citizenship
  37. Religious Studies
  38. Resistant Materials
  39. Science
  40. Sociology
  41. Spanish
  42. Systems and Control
  43. Textiles
  44. Welsh Second Language (WJEC)

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