If 27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy), then what is th

1.	If 27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy), then what is the value of (A + B - C)?1. 132. 163. 184. 11
Answer» Correct Answer - Option 2 : 16 Given : 27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy) Formula used : P³ - q³ = (p - q) (p² + q² + pq) Calculations : 27(x + y)³ - 8(x - y)³ = [3(x + y)]³ - [2(x - y)]³ we use given formula above ⇒ [3(x + y) - 2(x - y)] [(3x + 3y)² + (2x - 2y)² + 3(x + y) × 2(x - y)] ⇒ (x + 5y) (19x² + 7y² + 10xy) Now compare (x + 5y) (19x2 + 7y2 + 10xy) with (x + 5y)(Ax2 + By2 + Cxy) We will get A = 19, B = 7 and C = 10 So, A + B - C = 19 + 7 - 10 ⇒ 16 ∴ The value of A + B - C is 16

If 27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy), then what is the value of (A + B - C)?1. 132. 163. 184. 11

Answer» Correct Answer - Option 2 : 16

Given :

27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy)

Formula used :

P³ - q³ = (p - q) (p² + q² + pq)

Calculations :

27(x + y)³ - 8(x - y)³ = [3(x + y)]³ - [2(x - y)]³

we use given formula above

⇒ [3(x + y) - 2(x - y)] [(3x + 3y)² + (2x - 2y)² + 3(x + y) × 2(x - y)]

⇒ (x + 5y) (19x² + 7y² + 10xy)

Now compare (x + 5y) (19x2 + 7y2 + 10xy) with (x + 5y)(Ax2 + By2 + Cxy)

We will get A = 19, B = 7 and C = 10

So,

A + B - C = 19 + 7 - 10

⇒ 16

∴ The value of A + B - C is 16

Discussion

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