Question:
Factorize each of the following algebraic expression:
a2 + 4ab + 3b2
Solution:
$a^{2}+4 a b+3 b^{2}$
$=\mathrm{a}^{2}+4 \mathrm{ab}+4 \mathrm{~b}^{2}-\mathrm{b}^{2}$
$=\left[\mathrm{a}^{2}+2 \times \mathrm{a} \times 2 \mathrm{~b}+(2 \mathrm{~b})^{2}\right]-\mathrm{b}^{2}$
$=(\mathrm{a}+2 \mathrm{~b})^{2}-\mathrm{b}^{2}$
$=[(\mathrm{a}+2 \mathrm{~b})-\mathrm{b}][(\mathrm{a}+2 \mathrm{~b})+\mathrm{b}]$
$=(\mathrm{a}+2 \mathrm{~b}-\mathrm{b})(\mathrm{a}+2 \mathrm{~b}+\mathrm{b})$
$=(\mathrm{a}+\mathrm{b})(\mathrm{a}+3 \mathrm{~b})$
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