Question

How do you factor `4(x+3)^2-9(x-1)^2`?

Answer 1

This can be factored as a difference of squares.

Explanation:

Differences of squares are of the form `a^2-b^2=(a - b)(a + b)`. We can find the factors by finding the square roots of each part of the expression:

`sqrt(4(x+3)^2)=2(x+3)`

`sqrt(9(x-1)^2)=3(x-1)`

Thus, the expression can be factored into:

`= (2(x + 3) - 3(x - 1))(2(x + 3) + 3(x - 1))`

`=(2x+6-3x+3)(2x+6+3x-3)`

`=(9-x)(3+5x)`

Hopefully this helps!