Find the expansion of ${(3 p - 2 q + r)}^{2}$ .

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Solution

Using the form ${(a + b + c)}^{2}$ , where $a = 3 p, b = - 2 q, c = r$ .Thus
${(3 p - 2 q + r)}^{2} = {(3 p)}^{2} + {(- 2 q)}^{2} + r^{2} + 2 (3 p) (- 2 q) + 2 (- 2 q) r + 2 r (3 p) = 9 p^{2} + 4 q^{2} + r^{2} - 12 p q - 4 q r + 6 r p$

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