Question

How do you factor `7x^2-28`?

Answer 1

`7(x-2)(x+2)`

Explanation:

There is a `color(blue)"common factor"` of 7 in both terms which can be taken out.

`rArr7(x^2-4)tocolor(red)((1))`

`x^2-4" is a " color(blue)"difference of squares"` which is factorised in general as follows.

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

`"here " a=x" and " b=2`

`rArrx^2-4=(x-2)(x+2)`

going back to `color(red)((1))`

`rArr7x^2-28=7(x-2)(x+2)`

Answer 2

`= 7(x+2)(x-2)`

Explanation:

Always look for a common factor first.

It is `7` in this case.

`7x^2 -28 = 7(x^2-4)" "larr` this is the difference of squares.

`= 7(x+2)(x-2)`

The expression has 3 factors