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Question
Use the formula to expand the following:
(5) (3x − y)3
(5) (3x − y)3
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Solution
We know that (a −b)3 = a3 − 3a2b + 3ab2 − b3.
Comparing (3x − y)3 with (a − b)3, we get:
a = 3x and b = y
Substituting these in the above formula:
(3x − y)3 = (3x)3 − 3 × (3x)2 × y + 3 × 3x × y2 − (y)3
= 27x3 − 27x2y + 9xy2 − y3
Comparing (3x − y)3 with (a − b)3, we get:
a = 3x and b = y
Substituting these in the above formula:
(3x − y)3 = (3x)3 − 3 × (3x)2 × y + 3 × 3x × y2 − (y)3
= 27x3 − 27x2y + 9xy2 − y3
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