Question

factories the following:


x^2 - y^2 – 2y - 1​

Answer 1

:$x^{2} -y^{2} -2y-1\\x^{2}( -y2-2y-1)\\x^{2}( -y2-y-y-1)\\x^{2}( -y(y+1)-1(y+1))\\x^{2} ((y+1)(-y-1))\\(x+y+1)(x-y-1)$

Answer 2

☯GIVEN :

• $\bf{x^ 2 - y^2 - 2y-1}$ .

☯TO FIND :

• Factorised form.

☯FORMULA REQUIRED :

• $\bigstar \underline{ \boxed{ \red{\bf{ a^2+2ab+b^2 = {(a + b)}^{2} }}}}$

• $\bigstar \underline{ \boxed{ \red{\bf{ a^2 - b^2 = (a - b) (a + b) }}}}$

➲SOLUTION :

$\implies\sf{x^ 2 -y^ 2 - 2y - 1}$

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

• Used $\bf{ a^2+2ab+b^2 = {(a + b)}^{2}}$ .

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

• Used $\bf{ a^2 - b^2 = (a - b) (a + b)}$.

$\implies\sf{ \big[x -(y + 1) \big]\big[x + (y + 1)\big]}$

$\implies\underline{\boxed{\pink{\bf{(x - y - 1)(x + y + 1)}}}}$

▪Some important identities :

• $\bigstar \underline{ \boxed{ \green{\bf{ {(a - b)}^{2} = a^2 - 2ab + b^2 }}}}$

• $\bigstar \underline{ \boxed{ \green{\bf{ {(a +b)}^{2} = a^2 + 2ab + b^2 }}}}$

• $\bigstar \underline{ \boxed{ \green{\bf{ {(a +b)}^{0} = 1 }}}}$

• $\bigstar \underline{ \boxed{ \green{\bf{ {(a +b)}^{1} = a +b }}}}$