# How do you factor (x+1)^2+2(x+1)+1?

Jul 27, 2016

${\left(x + 2\right)}^{2}$.

#### Explanation:

Let us put $x + 1 = t$, then, the given

Expression$= {t}^{2} + 2 t + 1 = {\left(t + 1\right)}^{2}$

now, replacing $t$ by $x + 1$, we get,

The Exp.$= {\left(x + 1 + 1\right)}^{2} = {\left(x + 2\right)}^{2}$.

Otherwise, we can simplify the Exp. by expanding ${\left(x + 1\right)}^{2}$ and then factorise, as shown below :-

The Exp.$= {\left(x + 1\right)}^{2} + 2 \left(x + 1\right) + 1$

$= {x}^{2} + 2 x + 1 + 2 x + 2 + 1$

$= {x}^{2} + 4 x + 4$

$= {x}^{2} + 2 \cdot 2 \cdot x + {2}^{2}$

$= {\left(x + 2\right)}^{2}$, as before!

Enjoy Maths.!