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Question
Multiply and then evaluate:
(x2 – y) and (xy – y2); when x = 1 and y = 2.
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Solution
(x2 − y) × (xy − y2)
= x2 (xy − y2) − y (xy − y2)
= x3y − x2y2 − xy2 + y3
Verification:
When x = 1, y = 2
∴ L.H.S. = (x2 − y) (xy − y2)
= [(1)2 − 2] [1 × 2 − (2)2]
= (1 − 2) (2 − 4)
= − 1 × − 2
= 2
R.H.S. = x3y − x2y2 − xy2 + y3
= (1)3 × 2 − (1)2 (2)2 − 1(2)2 + (2)3
= 1 × 2 − 1 × 4 − 1 × 4 + 8
= 2 − 4 − 4 + 8
= 10 − 8
= 2
∴ L.H.S. = R.H.S.
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