Question

(4x - 2y)(x - 3y) = Ax2 + Bxy + Cy2. What are the values of A, B and C?

Answer 1

Answer:

This can be rewritten as (2*(x + y))3 - (x - y)3.

This is of the form a3 - b3 and the factorization of a3 - b3 is as given below.

a3 - b3 = (a-b) × (a2 + ab + b2)

Where a = 2(x + y) and b = (x - y). 

Substituting these in the above equation, we get

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

Expanding 2(x + y) × (x - y) + ((x - y))2, we get

= (2(x + y))2 + 2(x + y) × (x - y) + ((x - y))2

⇒ (4x2 + 4y2 + 8xy +2x2 - 2y2 + x2 + y2 - 2xy) 

⇒ 7x2 + 6xy + 3y2

Therefore,

8(x + y)3 - (x - y)3 = (x + 3y) × (7x2 + 6xy + 3y2).

Now the Value of (A - B - C) = 7 - 6 - 3

⇒ -2.

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