Question

(2x-y)³-(x+y)³+(2y-x)³​

Answer 1

Answer:

(2x+y)

3

+(2x−y)

3

⇒ [(2x)

2

]

3

−[(y)

2

]

3

[ Since, (a+b)(a−b)=a

2

−b

2

]

⇒ [4x

2

]

3

−[y

2

]

3

⇒ 64x

6

−y

6

∴ (2x+y)

3

+(2x−y)

3

=64x

6

−y

6

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Answer 2

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(2x-y)³ - (x+y)³ + (2y-x)³

➝ (2x-y)³ - (x+y)³ + (-x + 2y)³

➝ (2x-y)³ - (x+y)³ - (x - 2y)³ --------(1)

We know that,

(a-b)³ = a³ - b³ - 3ab (a-b)

(a + b)³ = a³ + b³ + 3ab (a+b)

Solving by properties,

(2x-y)³ = (2x)³ - (y)³ - 3×2x×y(2x-y)

➝ 8x³ - y³ - 6xy(2x-y)

➝ 8x³ - y³ - 12x²y + 6xy² --------(2)

(x+y)³ = (x)³ + (y)³ + 3xy ( x + y )

➝ x³ + y³ + 3x²y + 3xy² --------(3)

(x - 2y)³ = (x)³ - (2y)³ - 3×x×2y(x-2y)

➝ x³ - 8y³ - 6xy (x-2y)

➝ x³ - 8y³ - 6x²y + 12xy² --------(4)

Putting 2,3,4 in 1 ,

(2x-y)³ - (x+y)³ - (x - 2y)³

➝ 8x³ - y³ - 12x²y + 6xy² - (x³ + y³ + 3x²y + 3xy² ) - (x³ - 8y³ - 6x²y + 12xy²)

➝ 8x³ - y³ - 12x²y + 6xy² - x³ - y³ - 3x²y - 3xy² - x³ + 8y³ + 6x²y - 12xy²

➝ 8x³ - x³ - x³ - y³ - y³ + 2y³ - 12x²y -3x²y + 6x²y + 6xy² - 3xy² - 12xy²

➝ 8x³ - 2x³ - 2 y³ + 2y³ - 15x²y + 6x²y + 6xy² - 15xy²

➝ 6x³ + 4y³ - 9x²y - 9xy²

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