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Question
Simplify:
(a – 4b)3 + (4b – 3c)3 + (3c – а)3
Simplify
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Solution
Given expression: (a – 4b)3 + (4b – 3c)3 + (3c – а)3
Step-wise calculation:
1. Let x = a – 4b, y = 4b – 3c, z = 3c – a.
2. Calculate the sum (x + y + z):
(a – 4b) + (4b – 3c) + (3c – a) = a – 4b + 4b – 3c + 3c – a
(a – 4b) + (4b – 3c) + (3c – a) = 0
3. When (x + y + z = 0), the identity for cubes applies: x3 + y3 + z3 = 3xyz.
4. Therefore, (a – 4b)3 + (4b – 3c)3 + (3c – a)3 = 3(a – 4b)(4b – 3c)(3c – a).
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Chapter 3: Expansions - Exercise 3A [Page 65]
