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Year 8AC9M8A01

Expanding, Factorising and Simplifying

Create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties.

Expanding and factorising are the same move in opposite directions. Once you see that, factorising stops being guesswork.

Builds onYr 7 · Expanding Brackets

Method

Expanding removes brackets
3(x+4)=3x+123(x + 4) = 3x + 12
Multiply every term inside by what is outside.
Factorising puts them back
3x+12=3(x+4)3x + 12 = 3(x + 4)
Take out the highest common factor.
Watch a minus outside the bracket
2(x5)=2x+10-2(x - 5) = -2x + 10
It changes the sign of every term inside.
Collect like terms last
Expand first, then gather. Never both at once.

Worked example

e.g. Expand and simplify 4(2x3)2(x+5)\text{Expand and simplify } 4(2x - 3) - 2(x + 5)
  1. Expand the first bracket.8x128x - 12
  2. Expand the second. The minus outside changes both signs.2x10-2x - 10
  3. Write it all out with no brackets.8x122x108x - 12 - 2x - 10
  4. Collect the xx terms.8x2x=6x8x - 2x = 6x
  5. Collect the numbers.1210=22-12 - 10 = -22
  6. Write the answer.6x226x - 22

Practice

Expand fully before collecting. Take each sign with its term.

1
5(x+3)5(x + 3)
Answer5x+155x + 15
2
3(2a4)-3(2a - 4)
Answer6a+12-6a + 12
3
Factorise 6x+9\text{Factorise } 6x + 9
Answer3(2x+3)3(2x + 3)
4
Factorise 10y15\text{Factorise } 10y - 15
Answer5(2y3)5(2y - 3)
5
2(x+4)+3(x1)2(x + 4) + 3(x - 1)
Answer5x+55x + 5
6
Why is 3(x+4)=3x+4 wrong?\text{Why is } 3(x+4) = 3x + 4 \text{ wrong?}
AnswerThe 3 must multiply the 4 as well.\text{The 3 must multiply the 4 as well.}
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