Question

150. Find four nontrivial (not 1) factors in terms of y and y whose product is 8^2x- 27^2y.

Answer 1

Factoring the expression, we have:

`\begin{gathered} 8^(2x)-27^(2y) \\ (8^x)^2-(27^y)^(2y)\text{ (Rewriting the expression as a difference of squares)} \\ (8^x+27^y)(8^x-27^y)\text{ (Factoring as a as a difference of squares}) \\ ((2^3)^x+(3^3)^y)((2^3)^x-(3^3)^y)\text{ (Using prime factorization to modify the expression)} \end{gathered}`

The final answer is:

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