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CGPSC Prelims CSAT 2020 Solved Paper 2

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Question : 1 of 100

Marks: +1, -0

If

(x + y)^{3} + 8(x - y)^{3} = (3x + Ay) (3x^{2} + Bxy + Cy^{2}),

then the value of

(C - A + B)

will be:

0
3
2
4

Solution:

Concept:

Use the sum of cubes identity to factor the given expression.

Explanation:

Write

8(x-y)^3

as

[2(x-y)]^3

.

Let

a=x+y

and

b=2(x-y)

.

Then

a^3+b^3=(a+b)(a^2-ab+b^2)

.

So

(x+y)^3+8(x-y)^3=(x+y+2x-2y)\left((x+y)^2-(x+y)2(x-y)+[2(x-y)]^2\right)

.

Simplify the first factor:

x+y+2x-2y=3x-y

.

Compare with

(3x+Ay)

:

A=-1

.

Simplify the second factor:

(x+y)^2-(x+y)2(x-y)+4(x-y)^2

=x^2+2xy+y^2-2x^2+2y^2+4x^2-8xy+4y^2

=3x^2-6xy+7y^2

.

Compare with

3x^2+Bxy+Cy^2

:

B=-6

,

C=7

.

Thus,

C-A+B=7-(-1)+(-6)=2

.

Answer:

C-A+B=2

, so the correct option is C.

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