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

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Solution

$(2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$
Using identity $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$= 6.25 p^{2} - 7.5 p q + 2.25 q^{2} - (2.25 p^{2} - 7.5 p r + 6.25 q^{2})$
$= 6.25 p^{2} - 7.5 p q + 2.25 q^{2} - 2.25 p^{2} + 7.5 p q - 6.25 q^{2})$
$= 4 p^{2} - 4 q^{2}$

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