Question

Simplify

(2x-5y) ³-(2x+5y)³​

Answer 1

Step-by-step explanation:

(a + b) ³ = a³ + 3ab² + 3a²b + b³

this formula use for your problem

Answer 2

Answer:

(2x-5y)^3-(2x+5y)^3=-250y^3-120x^2y(2x−5y)3−(2x+5y)3=−250y3−120x2y

Step-by-step explanation:

Given : Expression (2x-5y)^3-(2x+5y)^3(2x−5y)3−(2x+5y)3

To find : Simplify the expression?

Solution :

Using cubic identity,

(a-b)^3=a^3+b^3-3ab(a-b)(a−b)3=a3+b3−3ab(a−b)

Applying identity in (2x-5y)^3(2x−5y)3

(2x-5y)^3=(2x)^3-(5y)^3-3(2x)(5y)(2x-5y)(2x−5y)3=(2x)3−(5y)3−3(2x)(5y)(2x−5y)

Applying identity in (2x+5y)^3(2x+5y)3

(2x+5y)^3=(2x)^3+(5y)^3+3(2x)(5y)(2x+5y)(2x+5y)3=(2x)3+(5y)3+3(2x)(5y)(2x+5y)

Substitute in expression,

(2x-5y)^3-(2x+5y)^3(2x−5y)3−(2x+5y)3

=(2x)^3-(5y)^3-3(2x)(5y)(2x-5y)-(2x)^3-(5y)^3-3(2x)(5y)(2x+5y)=(2x)3−(5y)3−3(2x)(5y)(2x−5y)−(2x)3−(5y)3−3(2x)(5y)(2x+5y)

=-125y^3-30xy(2x-5y)-125y^3-30xy(2x+5y)=−125y^3−30xy(2x−5y)−125y^3−30xy(2x+5y)

=-250y^3-60x^2y+150xy^2-60x^2y-150xy^2=−250y3−60x2y+150xy2−60x2y−150xy^2

=-250y^3-120x^2y=−250y^3−120x^2y

Therefore, (2x-5y)^3-(2x+5y)^3=-250y^3-120x^2y(2x−5y)3−(2x+5y)3=−250y^3−120x^2y