Question

What is the expression for the area of a rectangle whose length is $0.5p-0.25q$ and height is $4(2p+q)?$

• A. $2p^2-q^2$
• B. $2p^2+q^2$
• C. $4p^2-q^2$
• D. $4p^2+q^2$

Answer 1

The correct option is C $4p^2-q^2$

Area $=(0.5p-0.25q)\left(4\right(2p+q\left)\right)$
Area $=(\frac{1}{2}p-\frac{1}{4}q)\left(4\right(2p+q\left)\right)$
Multiplication is commutative.
$=4(\frac{1}{2}p-\frac{1}{4}q)(2p+q)$
$=(2p-q)(2p+q)=(2p{)}^2-(q{)}^2=4p^2-q^2$
As $(a+b)(a-b)=a^2-b^2$