If [8(x + y)3 - 27(x - y)3] ÷ (5y - x) = Ax2 + Bxy + Cy2 , then the value of (A + B + C) is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 16
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Concept |
Application |
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Formula: a3 - b3 = (a - b) (a2 + b2 + ab) |
[8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2 ⇒ [[2(x + y)]3 – [3(x – y)]3] ÷ (5y – x) = Ax2 + Bxy + Cy2 Using the formula: ⇒ [2(x + y) – 3(x – y)] [[2(x + y)]2 + [3(x – y)]2 + 2(x + y) × 3(x – y)] ÷ (5y – x) = Ax2 + Bxy + Cy2 ⇒ [5y – x] [4x2 + 8xy + 4y2 + 6x2 – 6y2 + 9x2 – 18xy + 9y2] ÷ (5y – x) = Ax2 + Bxy + Cy2 ⇒ 19x2 – 10xy + 7y2 = Ax2 + Bxy + Cy2 Comparing the coefficients: ⇒ A = 19, B = -10 and C = 7 Hence, A + B + C = 19 – 10 + 7 = 16 |