Question

simplify (2x-5y)^3-(2x+5y)^3

Answer 1

(2x-5y)³-(2x+5y)³
a³-b³ = (a-b)(a²+b²+ab)
=> (2x-5y-2x-5y)[{2x-5y}²+{2x+5y}²+(2x-5y)(2x+5y)]
=> -10y(4x²+25y²-20xy+ 4x²+25y²+20xy+4x²-25y²)

(a+b)(a-b) = a²-b²
-10y(12x²+25y²) is the answer
hope this helps

Answer 2

Answer:

$(2x-5y)^3-(2x+5y)^3=-250y^3-120x^2y$

Step-by-step explanation:

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

To find : Simplify the expression?

Solution :

Using cubic identity,

$(a-b)^3=a^3+b^3-3ab(a-b)$

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

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

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

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

Substitute in expression,

$(2x-5y)^3-(2x+5y)^3$

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

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

$=-250y^3-60x^2y+150xy^2-60x^2y-150xy^2$

$=-250y^3-120x^2y$

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