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Question
Simplify (5x – 3y)2 – (5x + 3y)2
Solution
We have the identities
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
So (5x – 3y)2 – (5x + 3y)2 = (5x)2 – (2 × 5x × 3y) + (3y)2
= 52x2 – 30xy + 32y2 – [52x2 – 30xy + 32y2]
= 25x2 – 30xy + 9y2 – [25x2 + 30xy + 9y2]
= 25x2 – 30xy + 9y2 – 25x2 – 30xy – 9y2
= x2(25 – 25) – xy(30 + 30) + y2(9 – 9)
= 0x2 – 60xy + 0y2 = – 60xy
∴ (5x – 3y)2 – (5x + 3y)2 = – 60xy
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