Question

simplify ( x + y + z )cube - ( x- y - z) cube​

Answer 1

Solution:

/* We know the algebraic identity:

a³-b³ = (a-b)³+3ab(a-b) */

Here ,

a = x+y+z , b = x-y-z

Now ,

a³-b³

= (a-b)³+3ab(a-b)

= [x+y+z-(x-y-z)]³+3(x+y+z)(x-y-z)[x+y+z-(x-y-z)]

= (x+y+z-x+y+z)³+3(x+y+z)[x-(y+z)](x+y+z-x+y+z)

= (2y+2z)³+3[x²-(y+z)²](2y+2z)

= (2y)³+(2z)³+12y²z+12yz²+3[x²-(y²+z²+2yz)](2y+2z)

= 8y³+8z³+12y²z+12yz²+3[x²-y²-z²-2yz)(2y+2z)

= 8y³+8z³+12y²z+12yz²+3(2x²y+2x²z-2y³-2y²z-2yz²-2z³-4y²z-4yz²)

= 8y³+8z³+12y²z+12yz²+6x²y+6x²z-6y³-6y²z-6yz²-6z³-12y²z-12yz²

= 2y³+2z³-6y²z-6yz²+6x²y+6x²z-12

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