Question

simplify（2x-5y）^3-（2x+5y）^3

Answer 1

hi mate,

solution: （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)]

[using identity, (a – b)^3 = a^3 -b^3 – 3ab

and

(a + b)^3 =a^3 +b^3 + 3ab]

= (2x)^3 – (5y)^3 – 30xy(2x – 5y) – (2x)^3– (5y)^3 – 30xy (2x + 5y)

= -2 (5y)^3 – 30xy(2x – 5y + 2x + 5y)

= -2 • 125y^3 – 30xy(4x)

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

and

(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)

i hope it helps you.