Show that $(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}$

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Solution

${(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2}$
using ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ and ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$
${(4 p q + 3 q)}^{2} = - {(4 p q - 3 q)}^{2} = 16 p^{2} q^{2} + 9 q^{2} + 24 p q^{2} - (16 p^{2} q^{2} + 9 q^{2} - 24 p q^{2}) = 48 p q^{2}$

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(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}

Prove that: $(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}$ .

(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}

{(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2} =

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