Question

Simplify (x+y)³-(x-y)³-6y(x²-y²)

Answer 1

I hope you got the answer..

Answer 2

AnswEr:

We have,

$\sf\red{(x+y)^3-(x-y)^3-6y(x^2-y^2)}$

$\tt = {(x + y)}^{3} - {(x - y)}^{3} - 3 \times 2y \times (x + y)(x - y) \\ \\ \tt = {[(x + y)}^{3} - {(x - y)]}^{3} - 3(x + y) - (x - y) \\ \tt(x + y)(x - y) \\ \\ \tt = {(x + y)}^{3} - {(x - y)}^{3} - 3(x + y)(x - y)[(x + y) - (x - y)] \\ \\ \tt = {a}^{3} - {b}^{3} - 3ab$

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$\sf\pink{Where\:a=x+y\:and\:b=x-y}$

$\sf = {(a - b)}^{3} = [(x + y) - (x - y)] {}^{3} \\ \\ \sf \leadsto \: {(2y)}^{3} = 8 {y}^{3}$

#BAL

#Answerwithquality