Question

Which of the binomials below is a factor of this expression?25x2 - 4y2z2 A. 5x – 2yzB. 5x2 - 2y2z2C. 5x - 4yzD..5x2 - 4y2z2

Answer 1

We can see in the expression 25x2 - 4y2z2 that each term is a perfect square:

25x2 is the square of 5x,

4y2z2 is the square of 2xz.

So we can factorate this expression using the following notable product:

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

Using a = 5x and b = 2yz, we have that:

$25x^2-4y^2z^2=(5x+2yz)(5x-2yz)$

So one factor is (5x + 2yz) and the other factor is (5x - 2yz).

Looking at the options, the correct one is A.