Question

Simplify :${\left(2.5p-1.5q\right)}^2-{\left(1.5p-2.5q\right)}^2$

Answer 1

Given ${\left(2.5p-1.5q\right)}^2-{\left(1.5p-2.5q\right)}^2$

Apply ${\left(a-b\right)}^2=a^2+b^2-2ab$:

$\begin{array}{l}{\left(2.5p-1.5q\right)}^2-{\left(1.5p-2.5q\right)}^2\\ ={\left(2.5p\right)}^2+{\left(1.5p\right)}^2-2\times 2.5p\times 1.5q-\left\{{\left(1.5p\right)}^2+{\left(2.5q\right)}^2-2\times 1.5p\times 2.5q\right\}\\ =6.25p^2+2.25p^2-7.5pq-2.25p^2-6.25q^2+7.5pq\\ =4p^2-4q^2\\ =4\left(p^2-q^2\right)\end{array}$

Hence the simplified form of ${\left(2.5p-1.5q\right)}^2-{\left(1.5p-2.5q\right)}^2$ is $4\left(p^2-q^2\right)$.