SOLUTION: please help reduce 64y^3+27z^3 / 4y+3z

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Question 63567: please help
reduce 64y^3+27z^3 / 4y+3z

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
reduce [64y^3+27z^3] / [4y+3z]
The numerator is the sum of cubes (4y)^3 + (3z)^3 and is
divisible by 4y+3z leaving a quotient of:
=[(4y)^2-(4y)(3z)+(3z)^2
=16y^2-12yz+9z^2
---------
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%2864y%5E3+%2B+27z%5E3%29+%2F+%284y+%2B+3z%29
%28%284y%29%5E3+%2B+%283z%29%5E3%29+%2F+%284y+%2B+3z%29
a = 4y
b = 3z
The equation is now in the form
%28a%5E3+%2B+b%5E3%29+%2F+%28a+%2B+b%29
If you do the long division, this equals
a%5E2+-ab+%2B+b%5E2 or
%284y%29%5E2+-+%284y%29%2A%283z%29+%2B+%283z%29%5E2
16y%5E2+-+12yz+%2B+9z%5E2 answer
You can check this by doing
%2816y%5E2+-+12yz+%2B+9z%5E2%29*%284y+%2B+3z%29
and seeing if it equals 64y%5E3+%2B+27z%5E3