Question 85 (xv)

Expand the following, using suitable identities.

$(0.9 p - 0.5 q)^{2}$

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Solution

We have,
$(0.9 p - 0.5 q)^{2} = (0.9 p)^{2} + (0.5 q)^{2} - 2 \times 0.9 p \times 0.5 q$
[using the identity, $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= 0.81 p^{2} + 0.25 q^{2} - 0.9 p q$

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