Question

factorise this equation-
(x+2)2+p2+2p(x+2).

Answer 1

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Answer 2

Answer:  The required factored form of the given expression is $(x+p+2)(x+p+2).$

Step-by-step explanation:  We are given to factorize the following quadratic expression :

$f(x)=(x+2)^2+p^2+2p(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following factorization formula :

$a^2+2ab+b^2=(a+b)^2.$

From (i), we get

$f(x)\\\\=(x+2)^2+p^2+2p(x+2)\\\\=(x+2)^2+2\times(x+2)\times p+p^2\\\\=(x+2+p)^2\\\\=(x+p+2)(x+p+2).$

Thus, the required factored form of the given expression is $(x+p+2)(x+p+2).$