Question

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

• A. 13
• B. 16
• C. 18
• D. 11

Answer 1

Answer:

B. 16

Solution:

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