SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]81x^4-16y^4[/tex]
STEP 2: Factorize the expression
[tex]\begin{gathered} 81x^4=(9x^2)^2 \\ 16y^4=(4y^2)^2 \end{gathered}[/tex]
We have:
[tex]\begin{gathered} =\left(9x^2\right)^2-\left(4y^2\right)^2 \\ \mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right) \\ \left(9x^2\right)^2-\left(4y^2\right)^2=\left(9x^2+4y^2\right)\left(9x^2-4y^2\right) \\ =\left(9x^2+4y^2\right)\left(9x^2-4y^2\right) \end{gathered}[/tex]
By further simplification, we have:
Factorize the second part:
[tex]\left(9x^2-4y^2\right)=\left(3x+2y\right)\left(3x-2y\right)[/tex]
Hence, the final factored form is given as:
[tex]\left(9x^2+4y^2\right)\left(3x+2y\right)\left(3x-2y\right)[/tex]
