Question

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

Answer 1

\[16 - a^6 + 4 a^3 b^3 - 4 b^6 \]

\[ = 16 - ( a^6 - 4 a^3 b^3 + 4 b^6 )\]

\[ = 4^2 - [( a^3 )^2 - 2 \times a^3 \times 2 b^3 + (2 b^3 )^2 ]\]

\[ = 4^2 - ( a^3 - 2 b^3 )^2 \]

\[ = [4 - ( a^3 - 2 b^3 )][4 + ( a^3 - 2 b^3 )]\]

\[ = (4 - a^3 + 2 b^3 )(4 + a^3 - 2 b^3 )\]

\[ = ( a^3 - 2 b^3 + 4)( - a^3 + 2 b^3 + 4)\]