Question

How do you factor `9m^2-144`?

Answer 1

`9(m-4)(m+4)`

Explanation:

The first step in factorising is to take out any `color(blue)"common factor"`

`rArr9m^2-144=9(m^2-16)larr" common factor of 9"`

Now `m^2-16" is a " color(blue)"difference of squares"` and is factorised, in general, as shown.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"For " m^2-16to a=m" and " b=4`

`rArrm^2-16=(m-4)(m+4)`

Putting it all together gives.

`rArr9m^2-144=9(m-4)(m+4)`