Question #62fe0

3 Answers
Jan 20, 2018

2x^2-18=2(x+3)(x-3)

Explanation:

First, we can bring out a 2 since both terms are a multiple of 2:
2x^2-18=2(x^2-9)

Next we realize that x^2-9 is a difference of squares. We know that the formula for difference of squares is:
(a+b)(a-b)=a^2-b^2

This means we can factor our expression like so:
2(x+3)(x-3)

Jan 20, 2018

2(x+3)(x-3)

Explanation:

First, we know that 18=9*2:
2x^2-9*2

Therefore, factor out the common term 2:
color(red)2x^2-9*color(red)2 to be equals to:

2(x^2-9)

Then, we rewrite 9 as 3^2:

2(x^2-3^2).

We will remove 2 for now.
We will then apply the DOS (Difference of squares) rule:
x^2-y^2=(x+y)(x-y)

Therefore, (x^2-3^2)=(x+3)(x-3)

Put back the 2:
2(x+3)(x-3)

Jan 20, 2018

2(x-3)(x+3)

Explanation:

It seems like there's nothing to be done here about the x^2. Let's start by factoring out the 2 to see if anything is "hidden".

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

x^2-9=x^2-3^2=(x-3)(x+3)

There's an identity for a difference of squares:

x^2-y^2=(x-y)(x+y)

On such problems, if "factoring out numbers" doesn't seem to work, maybe you'll have to use one of those.