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Question 5:
Simplify (2x – 5y)3 – (2x + 5y)3.
Answer 5:
Given that: (2x – 5y)3 – (2x + 5y)3.
= [(2x – 5y) – (2x + 5y)][ (2x – 5y)2 + (2x – 5y)(2x + 5y) + (2x + 5y)2]
[∵ a3 – b3 = (a – b)(a2 + ab + b2)]
= (–10y)[(4x2 + 25y2 – 20xy) + (4x2 – 25y2) + (4x2 + 25y2 + 20xy)]
[∵ (a + b)2 = (a2 + 2ab + b2), (a – b)2 = (a2 – 2ab + b2) ]
= (–10y)[(12x2 + 25y2]
= –120x2y – 250y3
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