Question

Expand ${(\sqrt{12}a+\sqrt{6}b)}^2$ using appropriate identity

Answer 1

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

Given:${(\sqrt{12}a+\sqrt{6}b)}^2$, apply the above identity taking $x=\sqrt{12}a$ and $y=\sqrt{6}b$

We get, ${(\sqrt{12}a+\sqrt{6}b)}^2={\left(\sqrt{12}a\right)}^2+{\left(\sqrt{6}b\right)}^2+(2\times \sqrt{12}a\times \sqrt{6}b)=12a^2+6b^2+12\sqrt{2}ab$

Hence, ${(\sqrt{12}a+\sqrt{6}b)}^2=12a^2+12\sqrt{2}ab+6b^2$.