Question

Consider the polynomial p(x) = 16x4 - 81y4. Which of the following are equivalent expressions?

Select all that apply.

Answer 1

Second expression and Last expression

Explanation:

Second expression and Last expression

1.
`(4x^2-9y^2)(4x^2-9y^2)`

`4x^2(4x^2-9y^2)-9y^2(4x^2-9y^2)`

`16x^4 -36x^2y^2 -36x^2y^2+81y^4`

`16x^4 -72x^2y^2+81y^4`

2.
`(4x^2-9y^2)(4x^2+9y^2)`

`4x^2(4x^2+9y^2)-9y^2(4x^2+9y^2)`

`16x^4+36x^2y^2-36x^2y^2-81y^4`

`16x^4-36y^4`

3.
`(4x^2+9y^2)(2x-3y)(2x-3y)`

`(4x^2+9y^2)(4x^2-6xy-6xy+9y^2)`

`(4x^2+9y^2)(4x^2-12xy+9y^2)`

`16x^4-48x^3y+36x^2y^2+36x^2y^2-108xy^3+81y^4`

`16x^4 -48x^3y+72x^2y^2-108y^3+81y^4`

4.
`(4x^2+9y^2)(2x+3y)(2x+3y)`

`(4x^2+9y^2)(4x^2+6xy+6xy+9y^2)`

`(4x^2+9y^2)(4x^2+12xy+9y^2)`

`16x^4+48x^3y+36x^2y^2+36x^2y^2+108xy^3+81y^4`

`16x^4+48x^3y+72x^2^2+108xy^3+81y^4`

5.
`(4x^2+9y^2)(2x+3y)(2x-3y)`

`(4x^2+9y^2)(4x^2-6xy+6xy-9y^2)`

`(4x^2+9y^2)(4x^2-9y^2)`

`16x^4-36x^2y^2+36x^2y^2-81y^4`

`16x^4-81y^4`

Hope this helps!