Question

Factorize each of the following algebraic expression:
a² + 4ab + 3b²

Answer 1

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