Question

$(\frac{2}{5}ab+c)(\frac{2}{5}ab-c)$ is equal to

• A. $\frac{4}{25}{a}^2{b}^2-\frac{4}{5}abc+c^2$
• B. $\frac{4}{25}{a}^2{b}^2+\frac{4}{5}abc+c^2$
• C. $\frac{4}{25}{a}^2{b}^2-c^2$
• D. $\frac{4}{25}{a}^2{b}^2+c^2$

Answer 1

Answer: (C)

$\frac{4}{25}{a}^2{b}^2-c^2$

$(\frac{2}{5}ab+c)(\frac{2}{5}ab-c)$

= $\frac{2}{5}ab(\frac{2}{5}ab-c)+c(\frac{2}{5}ab-c)$

= $\frac{4}{25}{a}^2{b}^2-\frac{2}{5}abc+\frac{2}{5}abc-c^2$

= $\frac{4}{25}{a}^2{b}^2-c^2$