Question

Simplify:

$(7m-8n{)}^2+(7m+8n{)}^2$.

• A. $198m^2+28n^2$
• B. $98m^2+128n^2$
• C. $98m+128n$
• D. $98m^2-128n^2$

Answer 1

Answer: (B)

Given, $(7m-8n{)}^2+(7m+8n{)}^2$.

We know, $(a-b{)}^2=a^2-2ab+b^2$
and $(a+b{)}^2=a^2+2ab+b^2$.

Then,

$(7m-8n{)}^2+(7m+8n{)}^2$

$=\left[\right(7m{)}^2-2\left(7m\right)\left(8n\right)+\left(8n{)}^2\right]+\left[\right(7m{)}^2+2\left(7m\right)\left(8n\right)+\left(8n{)}^2\right]$
$=(49m^2-112mn+64n^2)+(49m^2+112mn+64n^2)$
$=49m^2-112mn+64n^2+49m^2+112mn+64n^2$
$=98m^2+128n^2$.

Therefore, option $B$ is correct.