Question

Factorize the following:
a⁴b − 3a²b² − 6ab³

Answer 1

$$\begin{gathered} Thegreatestcommonfactoroftheterms{a}^{4}b,3a^2{b}^{2}and6a{b}^{3}oftheexpression{a}^{4}b-3a^2{b}^2-6a{b}^{3}isab. \\ Also,wecanwrite{a}^{4}b=ab\times a^3,3a^2{b}^2=ab\times 3aband6a{b}^3=ab\times 6b^2. \\ \therefore a^{4}b-3a^2{b}^2-6a{b}^3=ab\times a^3-ab\times 3ab-ab\times 6b^2 \\ =ab(a^3-3ab-6b^2) \end{gathered}$$