Question

Which of the following represents the factorization of the binomial below?25x² - 64y^2A. (5x-8y)(5x-8y)B. (5x-y)(x+8y)C. (5x-8y) (5x+8y)D. (5x+8y)(5x+8y)

Answer 1

The expression given is,

$25x^2-64y^2$

Factorize

$\begin{gathered} \mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right) \\ \left(5x\right)^2-\left(8y\right)^2=\left(5x+8y\right)\left(5x-8y\right) \\ =\left(5x+8y\right)\left(5x-8y\right) \end{gathered}$

Hence, Option C is the correct answer.