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

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Solution

L.H.S. $= (4 p q + 3 q)^{2} - (4 p q - 3 q)^{2}$

$= (4 p q + 3 q + 4 p q - 3 q) (4 p q + 3 q - 4 p q + 3 q)$
[Using identity $a^{2} - b^{2} = (a + b) (a - b)]$

$= (8 p q) (6 q)$

$= 48 p q^{2}$

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Show 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} = 48 p q^{2}

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

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