Question

Expand ${(3a-2b)}^2$ using appropriate identity

Answer 1

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

Given: ${(3a-2b)}^2$ we apply the above identity by taking

$x=3a$ and $y=-2b$

We get, ${(3a-2b)}^2={\left(3a\right)}^2+{\left(2b\right)}^2-(2\times 3a\times 2b)=9a^2+4b^2-12ab$

Hence, ${(3a-2b)}^2=9a^2-12ab+4b^2$.