Polynomials
asked Jul 16, 2015 in Algebra 1 Answers by jigs

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1 Answer

Can this be written -(125a^3-225a^2+135a-27)=-(5a-3)^3? Let's see:

(5a-3)^3=125a^3-(3(25a^2)*3+3(5a)*3^2-3^3)=

125a^3-225a^2+135a-27 (using the expansion of (x-y)^3=x^3-3x^2y+3y^2x-y^3, and putting x=5a and y=3). 

Yes! Good guess because 125=5^3 and 27=3^3 so it's worth a shot at assuming initially that we have a perfect cube.

So the answer is -(5a-3)^3 or (3-5a)^3 (these are equivalent because -(x^3)=(-x)^3.

answered Jul 16, 2015 by Rod Top Rated User (582,480 points)

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