Question

Factorize each of the following algebraic expression:
16 − a⁶ + 4a³b³ − 4b⁶

Answer 1

$$\begin{gathered} 16-a^6+4a^3{b}^3-4b^6 \\ =16-(a^6-4a^3{b}^3+4b^6) \\ =4^2-\left[\right(a^3{)}^2-2\times a^3\times 2b^3+\left(2b^3{)}^2\right] \\ =4^2-(a^3-2b^3{)}^2 \\ =[4-(a^3-2b^3)\left]\right[4+(a^3-2b^3)] \\ =(4-a^3+2b^3\left)\right(4+a^3-2b^3) \\ =(a^3-2b^3+4\left)\right(-a^3+2b^3+4) \end{gathered}$$