Consider the polynomial p(x) = 16x^4 81y^4. Which of the following are equivalent expressions? Select all that apply.
(4x²-9y^2)(4x² - 9y²)
(4x²-9y^2)(4x² + 9y²)
(4x²+9y^2)(2x-3y) (2x-3y)
(4x²+9y²) (2x + 3y) (2x + 3y)
(4x² +9y²) (2x + 3y)(2x - 3y)
Show your work
p(x) = 16x^4 - 81y^4
To determine which expressions are equivalent, we can factor p(x) using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)):
16x^4 - 81y^4 = (4x^2)^2 - (9y^2)^2
= (4x^2 + 9y^2)(4x^2 - 9y^2)
Therefore, the expressions that are equivalent to p(x) = 16x^4 - 81y^4 are:
- (4x²-9y^2)(4x² - 9y²)
- (4x²+9y^2)(2x-3y) (2x-3y)
- (4x²+9y²) (2x + 3y) (2x + 3y)
- (4x² +9y²) (2x + 3y)(2x - 3y)