Question

Simplify the expression:
$\frac{(7m-8n{)}^2(7m+8n{)}^2}{(7m{)}^2-(8n{)}^2}$

• A. $49m^2-64n^2$
• B. $49m^2+64n^2$
• C. $49m-64n$
• D. $49m+64n$

Answer 1

The correct option is A $49m^2-64n^2$

To Simplify: $\frac{(7m-8n{)}^2(7m+8n{)}^2}{(7m{)}^2-(8n{)}^2}$

By using the identity, $a^2-b^2=(a+b)(a-b)$ in the denominator, we get
​​​​​​​$\Rightarrow \frac{(7m-8n{)}^2(7m+8n{)}^2}{(7m-8n)(7m+n)}\Rightarrow (7m-8n)(7m+8n)\Rightarrow (7m{)}^2-(8n{)}^2\Rightarrow 49m^2-64n^2$