Question

Simplify: ${(xy+yz)}^2$ - ${(xy-yz)}^2$

• A. 4xy²
• B. 4xy²z
• C. 4xz
• D. -4xy²z

Answer 1

The correct option is B

4xy²z

For the expression ${(xy+yz)}^2$

We use the identity ${(a+b)}^2$ = $a^2$ + $b^2+2ab$

Hence we get $x^2$$y^2$ + $y^2$$z^2$ + 2xz$y^2$ ......................1;

For the expression ${(xy-yz)}^2$ we use the edentity ${(a-b)}^2$=$a^2$ + $b^2-2ab$

Hence we get $x^2$$y^2$ + $y^2$$z^2$ - 2xz$y^2$...........2;

Subtracting 2 from 1, we get:

($x^2$$y^2$ + $y^2$$z^2$ + ${2xyz}^2$) - ($x^2$$y^2$ + $y^2$$z^2-2xz{y}^2$) = $4x{y}^{2}z$