Question:
Factorize each of the following algebraic expression:
x2 + 2x + 1 − 9y2
Solution:
$x^{2}+2 x+1-9 y^{2}$
$=\left(x^{2}+2 x+1\right)-9 y^{2}$
$=\left(x^{2}+2 \times x \times 1+1\right)-9 y^{2}$
$=(x+1)^{2}-(3 y)^{2}$
$=[(x+1)-3 y][(x+1)+3 y]$
$=(x+1-3 y)(x+1+3 y)$
$=(x+3 y+1)(x-3 y+1)$
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