Algebra

Lesson

In Expanding Brackets we looked at how to use the distributive law to remove brackets from algebraic expressions. Now we are going to look at this process in reverse so we can *factorise* equations (which means writing them with brackets).

To factorise algebraic equations, we need to find the highest common factors (HCF) between the terms. We need to consider both the number values and algebraic terms.

**Factorise:** $12x+20$12`x`+20

**Think:** The highest common factor between $12x$12`x` and $20$20 is $4$4.

$4\times3x=12x$4×3`x`=12`x`

$4\times5=20$4×5=20

**Do:** $4\left(3x+5\right)$4(3`x`+5)

Remember to consider how the operators will change if negative numbers are involved.

**Factorise:** $-100r-20$−100`r`−20

**Think:** The HCF between $-100r$−100`r` and $-20$−20 is $-20$−20.

$-20\times5r=-100r$−20×5`r`=−100`r`

$-20\times1=-20$−20×1=−20

**Do:** $-20\left(5r+1\right)$−20(5`r`+1)

Factorise the expression $6v+30$6`v`+30.

Factorise the expression $-8v^2+56$−8`v`2+56.

Generalise the properties of operations with fractional numbers and integers.