Question

Factorise X square minus y square plus 2x plus 1

Answer 1

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SOLUTION

${x}^{2} - {y}^{2} + 2x + 1 \\ \\ {x}^{2} + {1}^{2} + 2x - {y}^{2} \\ \\ {(x + 1)}^{2} - {y}^{2} \\ \\ (x + 1 + y)(x + 1 - y)$

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Answer 2

Its factorised form is $(x-y+1)(x+1-y)$

Step-by-step explanation:

Since we have given that

$x^2-y^2+2x+1$

First we arrange it :

$x^2+2x+1-y^2\\\\=(x+1)^2-y^2$

As we know that

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

Now, we will do that

$a^2-b^2=(a+b)(a-b)$

So, it becomes,

$(x+1)^2-y^2\\\\=(x+1-y)(x+1+y)$

Hence, its factorised form is $(x-y+1)(x+1-y)$

# learn more:

Factorise a^2 - 64 factorise ​

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