Question

State whether True or False.

Multiply: $2x+\frac{1}{2}y$ and $2x-\frac{1}{2}y$.

The answer is $4x^2-\frac{1}{4}{y}^2$.

• A. True
• B. False

Answer 1

The correct option is A True

$(2x+\frac{1}{2}y)\times (2x-\frac{1}{2}y)$
$=2x(2x-\frac{1}{2}y)+\frac{1}{2}y(2x-\frac{1}{2}y)$
$=\left(2x\right)\left(2x\right)-2x\left(\frac{1}{2}y\right)+2x\left(\frac{1}{2}y\right)-\left(\frac{1}{2}y\right)\left(\frac{1}{2}y\right)$
$=(2x{)}^2-(\frac{1}{2}y{)}^2$
$=4x^2-\frac{1}{4}{y}^2$