Simplify: (2.5 p-1.5 q)^2-(1.5 p-2.5 q)^2 - Vidyadip

Question

Simplify: $ (2.5 p-1.5 q)^2-(1.5 p-2.5 q)^2 $

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Answer

To simplify, we will proceed as follows:
$ (2.5 p-1.5 q)^2-(1.5 p-2.5 q)^2 $
$=(2.5 p)^2+(1.5 q)^2-2(2.5 p)(1.5 q)-\left[(1.5 p)^2+(2.5 q)^2-2(1.5 p)(2.5 q)\right] $
$ =(2.5 p)^2-(1.5 p)^2+(1.5 q)^2-(2.5 q)^2 $
$ =[(2.5 p+1.5 p)(2.5 p-1.5 p)]+[(1.5 q+2.5)(1.5 q-2.5 q)] $
$ =4 p \times p+4 q \times(-q) $
$ =4 p^2-4 q^2 $
$ =4\left(p^2-4 q^2\right) $

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