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

1 Answer
Jul 27, 2016

Answer:

#(x+2)^2#.

Explanation:

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.!