Question

Simplify (2x-5y)^3-(2x+5y)^3​

Answer 1

QUESTION -

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

ANSWER -

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

=> [(2x-5y)-(2x+5y)] [(2x-5y)2 + (2x-5y)(2x+5y) + (2x+5y)2]

=> (2x-5y-2x-5y) [(4x2- 20xy + 25y2) +(4x2-25y2) + (4x2 + 20xy + 25y2)]

=> (-10y) (4x2- 20xy + 25y2 + 4x2-25y2 + 4x2 + 20xy + 25y2)

=> (-10y) (12x2 + 25y2 )

=> -120x2y -250xy2

Answer 2

Step-by-step explanation:

$it \: is \: in \: the \: form \: of \: a {}^{3} - b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} ) \\ \\ so(2x - 5y) {}^{3} - (2x + 5y) {}^{3} \\ \\ = (2x - 5y - 2x - 5y)((2x - 5y) {}^{2} + (2x - 5y )(2x + 5y) + (2x + 5y) {}^{2} \\ \\ = ( - 10y)(4x {}^{2} + 25y {}^{2} - 20xy + 4x {}^{2} - 25y {}^{2} + 4x {}^{2} + 25y {}^{2} + 20xy) \\ \\ = ( - 10y)(12x {}^{2} + 25y {}^{2} ) \\ \\ = - 120x {}^{2} - 250y {}^{2}$