Question

Factorize the following:
a⁴b − 3a²b² − 6ab³

Answer 1

\[\text{ The greatest common factor of the terms }a^4 b, 3 a^2 b^2\text{ and }6a b^3\text{ of the expression }a^4 b - 3 a^2 b^2 - 6a b^3\text{ is }ab . \]
\[\text{ Also, we can write }a^4 b = ab \times a^3 , 3 a^2 b^2 = ab \times 3ab\text{ and }6a b^3 = ab \times 6 b^2 . \]
\[ \therefore a^4 b - 3 a^2 b^2 - 6a b^3 = ab \times a^3 - ab \times 3ab - ab \times 6 b^2 \]
\[ = ab( a^3 - 3ab - 6 b^2 )\]