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