Question

Which binomial is a factor of 9x^2-64

Answer 1

(3x-8) or (3x+8) are binomials which are factors of the given expression

To get the binomial that is a factor of the given expression, we need to factorize the given expression

To do this, what we have to do is to use the difference of two squares

Given a^2 and b^2 as perfect squares separated by a negative sign, we have that;

`a^2-b^2\text{ = (a-b)(a+b)}`

Applying this to the question at hand, the factorization is;

`9x^2-64\text{ = (3x-8)(3x+8)}`

This means that either 3x-8 or 3x+8 are binomials which are factors of the given expression