Question

Factorize each of the following algebraic expression:
$x^2+2x+1-9y^2$

Answer 1

Given expression $x^2+2x+1-9y^2$
Here $x^2+2x+1$ is in the form of $a^2+2ab+b^2=(a+b{)}^2$
So, $x^2+2x\left(1\right)+(1{)}^2=(x+1{)}^2$
Thus, the expression can be written as
$x^2+2x+1-9y^2=(x+1{)}^2-9y^2$
$\Rightarrow x^2+2x+1-9y^2=(x+1{)}^2-(3y{)}^2$
Again from the formula of $a^2-b^2=(a+b)(a-b)$
$\Rightarrow x^2+2x+1-9y^2=\left[\right(x+1)+(3y\left)\right]\left[\right(x+1)-(3y\left)\right]$
Therefore, the factorized form of the given expression is $(x+3y+1)(x-3y+1)$