Question

What is te factorization of the expression below 9x^2-4y^2

Answer 1

The factorization of the expression $9 x^{2}-4 y^{2}$  is (3x+2y) (3x-2y).

Solution:

In the expression $9 x^{2}-4 y^{2}, 9 x^{2}$  can be written as $(3 x)^{2}$  . Similarly $4 y^{2}$  can be written as $(2 y)^{2}$  

$9 x^{2}-4 y^{2}=(3 x)^{2}-(2 y)^{2}$

Since both terms $(3 x)^{2}$  and $(2 y)^{2}$ are perfect squares, using the difference of squares formula,

$a^{2}-b^{2}=(a+b)(a-b)$

Here a = (3x) and b = (2y)

$(3 x)^{2}-(2 y)^{2}=(3 x+2 y)(3 x-2 y)$

(3x+2y)  and  (3x-2y)  are the factors of $9 x^{2}-4 y^{2}$