Question

Evaluate
${(\frac{3a}{2}-\frac{5b}{4})}^2$

Answer 1

Using the identity ${(x-y)}^2=x^2+y^2-2xy$

where $x=\frac{3a}{2},y=\frac{5b}{4}$

${(\frac{3a}{2}-\frac{5b}{4})}^2$

$={\left(\frac{3a}{2}\right)}^2+{\left(\frac{5b}{4}\right)}^2-2\times \frac{3a}{2}\times \frac{5b}{4}$

$=\frac{9a^2}{4}+\frac{25b^2}{16}-\frac{15ab}{4}$