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SSC CHSL 2019 PYQ — Question 55

SSC CHSL - 3rd July 2019 - Shift 3 • Quantitative Aptitude • Q55

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If 8(x + y)3 - (x - y)3 = (x + 3y) (Ax2 + Bxy + Cy2), then value of (A - B - C) is:

Show answer & explanation

Correct answer: A

Explanation

Correct Answer is option 1 i.e. -2

Application

Given:

8(x + y)3 - (x - y)3 = (x + 3y) (Ax2 + Bxy + Cy2)

8(x + y)3 - (x - y)3 can be written as:

⇒ [2(x + y)]3 – [x – y]3

Now, expanding it:

⇒ [2(x + y) – (x – y)] [(2(x + y))2 + 2(x + y) × (x - y) + (x - y)2]

⇒ [2x + 2y – x + y] [4x2 + 4y2 + 8xy + 2x2 – 2y2 + x2 + y2 – 2xy]

⇒ [x + 3y] [7x2 + 3y2 + 6xy]

Now,

(x + 3y) (Ax2 + Bxy + Cy2) = [x + 3y] [7x2 + 3y2 + 6xy]

Comparing the coefficients:

A = 7, B = 6 and C = 3

Hence,

(A – B – C) = 7 – 6 – 3 = -2