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Question
Expand the following:
(5x − 4y)3
Sum
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Solution
(5x − 4y)3
Using the identity:
(a − b)3 = a3 − 3a2b + 3ab2 − b3
Here, a = 5x, b = 4y
(5x − 4y)3 = (5x)3 − 3(5x)2(4y) + 3(5x)(4y)2 − (4y)3
= 125x3 − 3(25x2)(4y) + 3(5x)(16y2) − 64y3
= 125x3 − 3(100x2y) + 3(80xy2) − 64y3
∴ (5x − 4y)3 = 125x3 − 300x2y + 240xy2 − 64y3
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Chapter 3: Expansions - MISCELLANEOUS EXERCISE [Page 39]
