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(x+y)^2 + (x-y)^2 and (x+y)^2 - (x-y)^2

Question 4vSi...

Question

Question 4(v)
Simplify:
$(2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$

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Solution

$(2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$ $= (2.5 p)^{2} - 2 \times 2.5 p \times 1.5 q + (1.5 q)^{2} - [(1.5 p)^{2} - 2 \times 1.5 p \times 2.5 q + (2.5 q)^{2}]$
$[U s i n g i d e n t i t y (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
$= 6.25 p^{2} - 7.50 p q + 2.25 q^{2} - [2.25 p^{2} - 7.50 p q + 6.25 q^{2}]$ $= 6.25 p^{2} - 7.50 p q + 2.25 q^{2} - 2.25 p^{2} + 7.50 p q - 6.25 q^{2}$
$= 4 p^{2} - 4 q^{2}$

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