Question

Factor 36(a^2 - b^3)^4 - 18(a^2 - b^3)^7

Answer 1

Solution

We are required to factorize

$36(a^2-b^3)^4-18(a^2-b^3)^7$$=18(a^2-b^3)^4\text{ is a common factor}$$\begin{gathered} Thus,\text{ we have } \\ =18(a^2-b^3)^4(2-(a^2-b^3)^3) \end{gathered}$$\begin{gathered} Expand\text{ \lparen2-\lparen a}^2-b^2))^3 \\ =(2-a^6+3a^4b^3-3a^2b^6+b^9) \end{gathered}$

Thus, the answer is