Question

Factorise $z^2-(x^2+2xy+y^2)$ using identities.

• A. $(x+y-z)(z-x-y)$
• B. $(x+y+z)(z+x-y)$
• C. $(x+y+z)(z-x+y)$
• D. $(x+y+z)(z-x-y)$

Answer 1

The correct option is D $(x+y+z)(z-x-y)$

Given: $z^2-(x^2+2xy+y^2).$

Using the identity $(a+b{)}^2=a^2+2ab+b^2$ in the above equation we get,
$z^2-(x^2+2xy+y^2)=z^2-(x+y{)}^2$ . . . (i)

Using the identity $a^2-b^2=(a+b)(a-b)$ in (i) we get,
$z^2-(x+y{)}^2=[z+(x+y)\left]\right[z-(x+y)]$
$=(x+y+z)(z-x-y)$