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SSC Selection Post 2022 PYQ — Question 65

SSC Selection Post - Matriculation Level 2022 - 2 Feb 2022 - Shift 1 • Quantitative Aptitude • Q65

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[(4a - 5b)3 + (5b - 3c)3 - (4a - 3c)3] is equal to:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. -3(4a - 5b)(5b - 3c)(4a - 3c).

Let  x = 4a - 5b, y = 5b - 3c,  z = 4a - 3c

x + y = (4a - 5b) + (5b - 3c) = 4a - 3c = z

So the expression becomes  x3+y3−(x+y)3x^3 + y^3 - (x + y)^3

x3+y3−(x+y)3=−3xy(x+y)x^3 + y^3 - (x + y)^3 = -3xy(x + y) = -3(4a - 5b)(5b - 3c)(4a - 3c)