Factorizing the HCF

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.

Examples

Question 1

Factorise: $12x+20$12x+20 

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

          $4\times3x=12x$4×3x=12x 

            $4\times5=20$4×5=20

Do: $4\left(3x+5\right)$4(3x+5) 

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

 

Question 2

Factorise: $-100r-20$−100r−20 

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

$-20\times5r=-100r$−20×5r=−100r

       $-20\times1=-20$−20×1=−20

Do: $-20\left(5r+1\right)$−20(5r+1)

 

Question 3

Question 4