Question

Find ${\left(\frac{2}{3}a+\frac{3}{4}b\right)}^2$ by using suitable identity.

Answer 1

Given

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

It is in the form of

$(x+y{)}^2=x^2+2xy+y^2$

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

$=(\frac{2}{3}.a)+2.\frac{2}{3}a.\frac{3}{4}b+(\frac{3}{4}b{)}^2$

$=\frac{4}{9}.a^2+\frac{12}{12}ab+\frac{9}{16}.b^2$

$=\frac{4}{9}{a}^2+ab+\frac{9}{16}.b^2$