Question 84 (i)

Simplify

$(3 x + 2 y)^{2} + (3 x - 2 y)^{2}$

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Solution

We have
$(3 x + 2 y)^{2} + (3 x - 2 y)^{2} = (3 x)^{2} + (2 y)^{2} + 2 \times 3 x \times 2 y + (3 x)^{2} + (2 y)^{2} - 2 \times 3 x \times 2 y$
[using the identities, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ and $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= 9 x^{2} + 4 y^{2} + 12 x y + 9 x^{2} + 4 y^{2} - 12 x y = (9 x^{2} + 9 x^{2}) + (4 y^{2} + 4 y^{2}) + 12 x y - 12 x y = 18 x^{2} + 8 y^{2}$

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Question 84 (ii)

Simplify

$(3 x + 2 y)^{2} - (3 x - 2 y)^{2}$

Question 84 (i)

Simplify

$(3 x + 2 y)^{2} + (3 x - 2 y)^{2}$

Question 84 (ii)

Simplify

$(3 x + 2 y)^{2} - (3 x - 2 y)^{2}$

(3 x - 2 y)^{2} + 24 x y = (3 x + 2 y)^{2}

(3 x + 2 y)^{2} + (3 x - 2 y)^{2}

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