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Question
Write the following cube in expanded form:
(2a – 3b)3
Solution
It is known that,
(a + b)3 = a3 + b3 + 3ab(a + b) and (a − b)3 = a3 − b3 − 3ab(a − b)
(2a − 3b)3 = (2a)3 − (3b)3 – (3 × 2a × 3b)(2a – 3b)
= 8a3 – 27b3 – 18ab(2a – 3b)
= 8a3 – 27b3 – 36a2b + 54ab2
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