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Question
Use the formula to expand the following:
(6) (2 − 7b)3
(6) (2 − 7b)3
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Solution
We know that (x − y)3 = x3 − 3x2y + 3xy2 − y3.
Comparing (2 − 7b)3 with (x − y)3, we get:
x = 2 and y = 7b
Substituting these in the above formula:
(2 − 7b)3 = (2)3 − 3 × (2)2 × 7b + 3 × 2 × (7b)2 − (7b)3
= 8 − 84b + 294b2 − 343b3
Comparing (2 − 7b)3 with (x − y)3, we get:
x = 2 and y = 7b
Substituting these in the above formula:
(2 − 7b)3 = (2)3 − 3 × (2)2 × 7b + 3 × 2 × (7b)2 − (7b)3
= 8 − 84b + 294b2 − 343b3
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