# How do you factor 7x^2 -45?

The answer is (sqrt(7)x+sqrt(45))(sqrt(7)x−sqrt(45)) .
$\left(7 {x}^{2} - 45\right)$ fits the pattern of the difference of squares in which (a^2−b^2)=(a+b)(a−b) .
The factorization of (7x^2-45)=((sqrt(7)x)^2−(sqrt(45))^2)
Here $a = \sqrt{7} x$ , $b = \sqrt{45}$
So the factorization is (sqrt(7)x+sqrt(45))(sqrt(7)x−sqrt(45))