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Expanding and factorising brackets
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Expanding removes brackets; factorising puts them back. They are opposite processes.
Expanding
Multiply everything inside the bracket by the term outside.
3(x + 4) = 3x + 12
−2(y − 5) = −2y + 10 (a negative times a negative is positive)
x(x + 5) = x2 + 5x
3(x + 4) = 3x + 12
−2(y − 5) = −2y + 10 (a negative times a negative is positive)
x(x + 5) = x2 + 5x
Expand and simplify
Expand each bracket, then collect like terms.
2(x + 3) + 4(x − 1) = 2x + 6 + 4x − 4 = 6x + 2
2(x + 3) + 4(x − 1) = 2x + 6 + 4x − 4 = 6x + 2
Factorising
Take out the highest common factor.
6x + 15 = 3(2x + 5)
x2 + 5x = x(x + 5)
Check by expanding your answer.
6x + 15 = 3(2x + 5)
x2 + 5x = x(x + 5)
Check by expanding your answer.
Factorise 8a + 12 fully.
- The HCF of 8a and 12 is 4
- 8a ÷ 4 = 2a and 12 ÷ 4 = 3
Answer: 4(2a + 3)
Expand by multiplying every term inside by the term outside. Factorise by taking out the highest common factor, and check by expanding.
The interactive lesson includes the diagrams for this topic.
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