Question

5x10?+ 4x10°+ 3x10?+1​

Answer 1

Explanation:

(2x−5y)

3

−(2x+5y)

3

=−250y

3

−120x

2

y

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

=a

3

+b

3

−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=−250y

3

−60x

2

y+150xy

2

−60x

2

y−150xy

2

=-250y^3-120x^2y=−250y

3

−120x

2

y

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

3

−(2x+5y)

3

=−250y

3

−120x

2

y