Question

Find the value of expression $36x^2+64y^2+96xy$, When $x=\frac{2}{3}$ and $y=\frac{3}{4}$.

• A. $100$
• B. $10$
• C. $1000$
• D. $50$

Answer 1

The correct option is A $100$

Given expression is
$36x^2+64y^2+96xy$
On simplifying we get,
$=(6x{)}^2+(8y{)}^2-2\times \left(6x\right)\times \left(8y\right)$
$=(6x+8y{)}^2$
$[\because a^2+b^2+2ab=(a+b{)}^2]$
Putting values of $x=\frac{2}{3}$ and $y=\frac{3}{4}$ we get,
$=(6\times \frac{2}{3}+8\times \frac{3}{4}{)}^2$
$=(4+6{)}^2=(10{)}^2=100$