Julia P.

asked • 02/14/17

Algebra help

125x^3+27y^3 

Andrew M.

This is the sum of 2 cubes:
125x^3 = (5x)^3
27y^3 = (3y)^3
 
So;  125x^3 + 27y^3 = (5x)^3 + (3y)^3
 
But what are you trying to find?  You haven't told
us what you are being asked to do with this expression.
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02/14/17

Julia P.

Factoring the equation, thanks. 
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02/14/17

1 Expert Answer

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Andrew M. answered • 02/14/17

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Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

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Assuming the point is to factor this expression:
 
125x^3 + 27y3 = (5x)3 + (3y)3
 
Sum of two cubes formula:
a3 + b3 = (a+b)(a2-ab+b2)
For this expression a=5x, b=3y
 
125x3 + 27y3 = (5x+3y)[(5x)2 - (5x)(3y) + (3y)2]
 
= (5x + 3y)(25x2 - 15xy + 9y2)
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