Question

How do you use the difference of two squares formula to factor `2x^2 − 18`?

Answer 1

You know that `a^2-b^2=(a+b)(a-b)`
In your case
`(2x^2-18)=(xsqrt(2)+sqrt(18))(xsqrt(2)-sqrt(18))=`
`=(xsqrt(2)+sqrt(9*2))(xsqrt(2)-sqrt(9*2))=`
`=(xsqrt(2)+3sqrt(2))(xsqrt(2)-3sqrt(2))=`
`=sqrt(2)(x+3)sqrt(2)(x-3)=2(x+3)(x-3)`

Answer 2

To factor using integers, we may first remove the common factor of `2`. That will leave a difference of perfect squares.

`2x^2-18=2(x^2-9)=2(x^2-3^2)`

`=2(x+3)(x-3)`