Question

(v) x²-1-2y-y² fectorise the expression​

Answer 1

Answer:

${x}^{2} - 1 - 2y - {y}^{2} \\ = {x}^{2} - \{1 + 2y + {y}^{2} \} \\ = {x}^{2} - \{{y}^{2}+ 2y + 1 \} \\ = {x}^{2} - (y + 1)^{2} \\ = (x + y + 1)(x - y - 1) \: are \: the \: \\ required \: factors \: of \: the \: give \: expression.$

Answer 2

Answer:

$\Huge \boxed{(x+y+1)(x-y-1)}$

Step-by-step explanation:

To solve this problem, first you have to find the factor expression of x²-1-2y-y².

Remember to use distributive property of $\displaystyle a(b+c)=ab+ac$.

First, factor it out.

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

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

Next, factor it out again.

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

Therefore, the correct answer is (x+y+1)(x-y-1).

Hope this helps!

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