Question 84 (vi)

Simplify

$(2.5 m + 1.5 q)^{2} + (2.5 m - 1.5 q)^{2}$

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Solution

We have,
$(2.5 m + 1.5 q)^{2} + (2.5 m - 1.5 q)^{2} = (2.5 m)^{2} + (1.5 q)^{2} + 2 \times 2.5 m \times 1.5 q + (2.5 m)^{2} + (1.5 q)^{2} - 2 \times (2.5 m) \times (1.5 q)$
[using the identities, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ and $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= 6.25 m^{2} + 2.25 q^{2} + 6.25 m^{2} + 2.25 q^{2} = (6.25 + 6.25) m^{2} + (2.25 + 2.25) q^{2} = 12.5 m^{2} + 4.5 q^{2}$

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Question 84 (vi)

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