Question

Completely factor the difference of two squares

18-50z^2

Answer 1

Since both 18 and -50 are even, we can start by factoring a 2 out of the expression:

`18-50z^2=2(9-25z^2)`

To factor
`9-25z^2`, we can use the fact that, in general:

`a^2-b^2=(a+b)(a-b)` for any two numbers a and b. Since 9 = 3² and 25z² = (5z)², we can rewrite and factor our expression using this fact:

`9-25z^2=3^2-(5z)^2=(3+5z)(3-5z)`

Altogether, our expression becomes

`2(3+5z)(3-5z)`