Question

Simplify: $(\frac{p}{2}-\frac{p^3}{4})(\frac{p}{2}+\frac{p^3}{4})$.

• A. $\frac{p^2}{4}-\frac{p^6}{16}$
• B. $\frac{p^2}{4}+\frac{p^6}{16}$
• C. $\frac{p^2}{4}-\frac{p^6}{4}$
• D. $\frac{p^2}{4}+\frac{p^6}{4}$

Answer 1

The correct option is A $\frac{p^2}{4}-\frac{p^6}{16}$

Using the FOIL rule.
F=First terms, O= Outside terms, I = Inside terms, L= Last terms.

$(\frac{p}{2}-\frac{p^3}{4})(\frac{p}{2}+\frac{p^3}{4})$

$=\frac{p}{2}(\frac{p}{2}+\frac{p^3}{4})-\frac{p^3}{4}(\frac{p}{2}+\frac{p^3}{4})$

$=\frac{p^2}{4}+\frac{p^4}{8}-\frac{p^4}{8}-\frac{p^6}{16}$

$=\frac{p^2}{4}-\frac{p^6}{16}$ $(\because \frac{p^4}{8}-\frac{p^4}{8}=0)$

This is the required expression obtained using FOIL rule.

Also we can use the identity,
$(a+b)(a-b)=a^2-b^2$.