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

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Answer 1 · 2016-07-27T07:39:02

$(x+2)^2$ .

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

Expression $=t^2+2t+1=(t+1)^2$

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

The Exp. $=(x+1+1)^2=(x+2)^2$ .

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

The Exp. $=(x+1)^2+2(x+1)+1$

$=x^2+2x+1+2x+2+1$

$=x^2+4x+4$

$=x^2+2*2*x+2^2$

$=(x+2)^2$ , as before!

Enjoy Maths.!

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