Question

$(\frac{1}{5}x-\frac{1}{6}y)(5x+6y)$ is equal to

• A. $x^2-\frac{11xy}{30}-y^2$
• B. $x^2+\frac{11xy}{30}-y^2$
• C. $x^2+\frac{11xy}{30}+y^2$
• D. $x^2-\frac{11xy}{30}+y^2$

Answer 1

The correct option is B $x^2+\frac{11xy}{30}-y^2$

Required multiplication
$=(\frac{1}{5}x-\frac{1}{6}y)(5x+6y)$
$=\frac{1}{5}x(5x+6y)-\frac{1}{6}y(5x+6y)$
$=\left(\frac{1}{5}x\right)\left(5x\right)+\left(\frac{1}{5}x\right)\left(6y\right)+(-\frac{1}{6}y)\left(5x\right)+(-\frac{1}{6}y)\left(6y\right)$
$=x^2+\frac{6}{5}xy-\frac{5}{6}xy-y^2$

$=x^2+\frac{36xy-25xy}{30}-y^2$

$=x^2+\frac{11xy}{30}-y^2$