Question

Factorize using suitable identities:
(X+1) ^2-8(x+1) +16

Answer 1

Answer:

$\bold\red{{(x-3)}^{2}}$

Step-by-step explanation:

Given,

${(x + 1)}^{2} - 8(x + 1) + 16$

Let us take,

$(x + 1) = y$

Therefore,

we get,

$= {y}^{2} - 8y + 16$

Now,

After middle term splitting,

we get,

$= {y}^{2} - 4y - 4y + 16$

Taking common terms,

we get,

$= y(y - 4) - 4(y - 4) \\ \\ = (y - 4)(y - 4) \\ \\ = {(y - 4)}^{2}$

Putting the value of$y = ( x+1 ),$

we get,

$= {(x + 1 - 4)}^{2} \\ \\ = \bold{ {(x - 3)}^{2} }$