Question

USC
Simplify (2x + 5y)^3-(2x + 5y)^3​

Answer 1

EXPLANATION.

Method = 1.

⇒ (2x + 5y)³ - (2x + 5y)³.

As we know that,

Formula of :

⇒ (x + y)³ = x³ + 3x²y + 3xy² + y³.

Using this formula in equation and simplify the equation, we get.

⇒ [(2x)³ + 3(2x)²(5y) + 3(2x)(5y)² + (5y)³] - [(2x)³ + 3(2x)²(5y) + 3(2x)(5y)² + (5y)³].

⇒ [8x³ + 30x²y + 30xy² + 125y³] - [8x³ + 30x²y + 30xy² + 125y³].

⇒ 8x³ + 30x²y + 30xy² + 125y³ - 8x³ - 30x²y - 30xy² - 125y³.

⇒ 8x³ - 8x³ + 30x²y - 30x²y + 30xy² - 30xy² + 125y³ - 125y³.

⇒ 0.

(2x + 5y)³ - (2x - 5y)³ = 0.

Method = 2.

⇒ (2x + 5y)³ - (2x + 5y)³.

As we know that,

Formula of :

⇒ (x³ - y³) = (x - y)(x² + xy + y²).

Using this formula in equation and simplify the equation, we get.

⇒ [(2x + 5y) - (2x + 5y)][(2x + 5y)² + (2x + 5y)(2x + 5y) + (2x + 5y)²].

⇒ [2x + 5y - 2x - 5y][4x² + 25y² + 20xy + 4x² + 10xy + 10xy + 25y² + 4x² + 25y² + 20xy].

⇒ [0][12x² + 75y² + 60xy].

⇒ 0.

⇒ (2x + 5y)³ - (2x + 5y)³ = 0.

Answer 2

Step-by-step explanation:

Correct Question:— Simplify: (2x - 5y)^3-(2x + 5y)^3

Solution:—

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

∴ (2x - 5y)^3 - (2x + 5y)^3

= {(2x - 5y) - (2x + 5y)} × {(2x - 5y)^2 + (2x - 5y) + (2x + 5y) + (2x + 5y)^2}

= (-10y)(12x^2 + 25y^2)

= -120x^2y - 250y^3 Ans.

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