Question

Simplify: ${(4a-7b)}^2-{\left(3a\right)}^2$

Answer 1

Given expression is ${(4a-7b)}^2-{\left(3a\right)}^2$

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

${(4a-7b)}^2-{\left(3a\right)}^2=[{\left(4a\right)}^2+{\left(7b\right)}^2-(2\times 4a\times 7b)]-9a^2$

$=16a^2+49b^2-56ab-9a^2$

$=7a^2+49b^2-56ab$

$=7(a^2+7b^2-8ab)$

Hence, ${(4a-7b)}^2-{\left(3a\right)}^2=7(a^2+7b^2-8ab)$.