Question

Simplify $(xy+yz{)}^2-2x^2{y}^{2}z.$
Find the value when $x=-1,y=1$ and $z=2$.

• A. 3
• B. 4
• C. -3
• D. 0

Answer 1

The correct option is C

-3

Simplifying ${(xy+yz)}^2$ using the identity
${(a+b)}^2=a^2+b^2+2ab$
We get,
${(xy+yz)}^2=x^2{y}^2+y^2{z}^2+{2xzy}^2$

Therefore,
${(xy+yz)}^2-2x^2{y}^{2}z=x^2{y}^2+y^2{z}^2+2xz{y}^2-2x^2{y}^{2}z$

Placing the values of $x$,$y$ and $z$ in the above expression, we get
$1+4-4-4=-3$