Question 5(i)
Show that:
$(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}$

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Solution

$L H S = (3 x + 7)^{2} - 84 x$
$= (3 x)^{2} + 2 \times 3 x \times 7 + (7)^{2} - 84 x$ $[U s i n g i d e n t i t y (a + b)^{2} = a^{2} + 2 a b + b^{2}]$
$= 9 x^{2} + 42 x + 49 - 84 x = 9 x^{2} - 42 x + 49$
$(3 x)^{2} - 2 \times 3 \times 7 + (7)^{2}$
$= (3 x - 7)^{2}$ $[∵ (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
=R.H.S

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Question 5(i)
Show that:
$(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}$

{(3 x + 7)}^{2} - 84 x = {(3 x - 7)}^{2}

prove that:

{(3 x + 7)}^{2} - {(3 x - 7)}^{2} = 84 x

(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}

(i) {(3 x + 7)}^{2} - 84 x = {(3 x - 7)}^{2}

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

(i i i) (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

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