Question

Consider the polynomial p(x) = 16x^4 - 81. Which of the following are equivalent expressions? Select all that apply

Answer 1

(4x² + 9y²)(4x² - 9y²)

(4x² + 9y²)(2x-3y)(2x+3y)

Explanation:

This polynomial is a difference of squares. This means both its terms are perfect squares and can be factored using the square root of each term. When factoring by difference of squares, use the pattern a² - b² = (a-b)(a+b).

`16x^4 - 81y^4\\(4x^2-9y^2)(4x^2+9y^2)\\`

One of the factors is again a difference of squares 4x² - 9y².Repeat to factor.

(4x² + 9y²)(2x-3y)(2x+3y)