75
Question
Use the formula to expand the following:
(4) (8 − 5n)3
(4) (8 − 5n)3
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Solution
We know that (x − y)3 = x3 − 3x2y + 3xy2 − y3.
Comparing (8 − 5n)3 with (x − y)3, we get:
x = 8 and y = 5n
Substituting these in the above formula:
(8 − 5n)3 = (8)3 − 3 × (8)2 × 5 + 3 × 8 × (5n)2 − (5n)3
= 512 − 960n + 600n2 − 125n3
Comparing (8 − 5n)3 with (x − y)3, we get:
x = 8 and y = 5n
Substituting these in the above formula:
(8 − 5n)3 = (8)3 − 3 × (8)2 × 5 + 3 × 8 × (5n)2 − (5n)3
= 512 − 960n + 600n2 − 125n3
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