(Factorization) How can I factorize this?

Question

I'm not sure about how to factorise this. I'd appreciate some help. Thanks! $(12x-y)^2-(4x-3y)^2$.

Answer 1

Hint: You have something of the form $a^2-b^2=(a-b)(a+b)$.

Answer 2

Let $A = 12x - y$ and $B = 4x - 3y$. Then the expression becomes $$A^2 - B^2 = (A+B)(A-B) = ((12x-y) + (4x-3y)) ((12x-y) - (4x-3y)) = (16x - 4y) (8x + 2y) = 8 (4x-y) (4x+y)$$

Answer 3

$$ (12x - y)^2 - (4x - 3y)^2 = [12x - y - 4x + 3y][12x - y + 4x - 3y] = (8x+2y)(16x - 4y)$$