What is the expansion of $(4 p - 3 q)^{2}$ ?

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Solution

Here we use $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ .
Taking $a = 4 p$ and $b = 3 q$ ,
we obtain $(4 p - 3 q)^{2} = (4 p)^{2} - 2 (4 p) (3 q) + (3 q)^{2} = 16 p^{2} - 24 p q + 9 q^{2}$

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