Question

Expand ${(\sqrt{10}x-\sqrt{5}y)}^2$ using appropriate identity

Answer 1

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

Given: ${(\sqrt{10}x-\sqrt{5}y)}^2$ we apply the above identity by taking $x=\sqrt{10}x$ and $y=-\sqrt{5}y$:

We get, ${(\sqrt{10}x-\sqrt{5}y)}^2={\left(\sqrt{10}x\right)}^2+{\left(\sqrt{5}y\right)}^2-(2\times \sqrt{10}x\times \sqrt{5}y)=10x^2+5y^2-2\sqrt{50}xy=10x^2+5y^2-10\sqrt{2}xy$

Hence, ${(\sqrt{10}x-\sqrt{5}y)}^2=10x^2-10\sqrt{2}xy+5y^2$.