Question

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

Answer 1

Answer:

options (B) and (E) are correct.

$16x^2-81y^2=(4x^2+9y^2)(4x^2-9y^2)=(4x^2+9y^2)(2x-3y)(2x+3y)$

Step-by-step explanation:

The given polynomial , $16x^4-81y^4$

We have to choose an equivalent fraction from the given options,

Consider the given polynomial,

$16x^4-81y^4$ can be written as $(4x^2)^2-(9y^2)^2$

Applying identity, $a^2-b^2=(a+b)(a-b)$ , we get,

$(4x^2)^2-(9y^2)^2=(4x^2+9y^2)(4x^2-9y^2)$

Again appplying the same identity on second bracket we get,

$(4x^2+9y^2)(4x^2-9y^2)=(4x^2+9y^2)((2x)^2-(3y)^2)$

Thus, $(4x^2+9y^2)((2x)^2-(3y)^2)=(4x^2+9y^2)(2x-3y)(2x+3y)$

Thus, out of given options , options (B) and (E) are correct.

Answer 2

Hello :
p(x)=16x^4-81y^4 = (4x²)²-(9y²)² = (4x²-9y²)(4x²+9y²)...(answer :B)