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

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Solution

L.H.S = $(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2}$
$= (4 p q)^{2} + 2 \times 4 p q \times 3 q + (3 q)^{2} - [(4 p q)^{2} - 2 \times 4 p q \times 3 q + (3 q)^{2}]$ (1 mark)
$[U s i n g i d e n t i t i e s (a + b)^{2} = a^{2} + 2 a b + b^{2} a n d (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
$= 16 p^{2} q^{2} + 24 p q^{2} + 9 q^{2} - [16 p^{2} q^{2} - 24 p q^{2} + 9 q^{2}]$ (0.5 mark) $= 16 p^{2} q^{2} + 24 p q^{2} + 9 q^{2} - 16 p^{2} q^{2} + 24 p q^{2} - 9 q^{2}$ (0.5 mark)
$= 48 p q^{2}$
= R.H.S (1 mark)

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

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}

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