Question

If (x+y)³-(x-y)³-6y(x²-y²)=ky² then k=
A. 1
B. 2
C. 4
D. 8

Answer 1

Given:  (x + y)³ - (x - y)³ - 6y(x² - y²) = ky³  

 

In order to factorise the given algebraic expression we use the following Identity - = (a + b)³ = a³ + b³ + 3a²b + 3ab² & (a - b)³ = a³ - b³ - 3a²b + 3ab² :  

= x³ + y³ + 3x²y + 3xy² - (x³ - y³ - 3x²y + 3xy²) - 6y(x² - y²) = ky³

= x³ + y³ + 3x²y + 3xy² - x³ + y³ + 3x²y - 3xy² - 6x²y + 6y³ = ky³

= x³ - x³ + y³ + y³ + 6y³  + 3x²y + 3x²y - 6x²y + 3xy² - 3xy² = ky³

= 2y³ + 6y³ = ky²³

= 8y³ = ky³

On comparing :  

= k = 8

Hence, the value of k is 8.

Option (D)  8 is correct.

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Similar questions :

(x+y)³-(x-y)³ can be factorized as:

A. 2y(3x² +y² )

B. 2x(3x² +y² )

C. 2y(3y² +x² )

D. 2x(x² +3y² )

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The factors of x³-x²y-xy²+y³ are

A. (x+y)(x²-xy+y²)

B. (x+y)(x²+xy+y²)

C. (x+y)²(x-y)

D. (x-y)²(x+y)

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Answer 2

Identity to be used:-

x³ - y³ = (x - y) (x² + y² + xy)

=> (x + y)³ - (x - y)³ - 6y(x² - y²) = ky³

=> (x + y - x + y) ((x + y)² + (x - y)² + (x + y)(x - y)) = ky³

=> 2y (x² + y² + 2xy + x² + y² - 2xy + x² - y²) = ky³

=> 6x²y + 2y³ - 6x²y + 6y³ = ky³

=> 8y³ = ky³

Thus, k = 8

Option (D) 8 is correct.