Answer:
options (B) and (E) are correct.
[tex]16x^2-81y^2=(4x^2+9y^2)(4x^2-9y^2)=(4x^2+9y^2)(2x-3y)(2x+3y)[/tex]
Step-by-step explanation:
The given polynomial , [tex]16x^4-81y^4[/tex]
We have to choose an equivalent fraction from the given options,
Consider the given polynomial,
[tex]16x^4-81y^4[/tex] can be written as [tex](4x^2)^2-(9y^2)^2[/tex]
Applying identity, [tex]a^2-b^2=(a+b)(a-b)[/tex] , we get,
[tex](4x^2)^2-(9y^2)^2=(4x^2+9y^2)(4x^2-9y^2)[/tex]
Again appplying the same identity on second bracket we get,
[tex](4x^2+9y^2)(4x^2-9y^2)=(4x^2+9y^2)((2x)^2-(3y)^2)[/tex]
Thus, [tex](4x^2+9y^2)((2x)^2-(3y)^2)=(4x^2+9y^2)(2x-3y)(2x+3y)[/tex]
Thus, out of given options , options (B) and (E) are correct.
