Question 84 (xi)

Simplify

$(4.5 a + 1.5 b)^{2} + (4.5 b + 1.5 a)^{2}$

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Solution

We have, $(4.5 a + 1.5 b)^{2} + (4.5 b + 1.5 a)^{2}$
$= (4.5 a)^{2} + (1.5 b)^{2} + 2 \times 4.5 a \times 1.5 b + (4.5 b)^{2} + (1.5 a)^{2} + 2 \times 4.5 b \times 1.5 a$ [using the identity, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ]
$= 20.25 a^{2} + 2.25 b^{2} + 13.5 a b + 20.25 b^{2} + 2.25 a^{2} + 13.5 a b = 22.5 a^{2} + 22.5 b^{2} + 27 a b$

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Question 84 (xi)

Simplify

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