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Q&A #849


Factoring the sum and difference of two cubes

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 29, 1998 at 21:48:08
Subject: Re: Factoring the sum and difference of two cubes

If you are a teacher and wish to show how to do this:

Divide (x^3 + y^3) by (x + y) using long division. The answer is: (x^2 - xy +
y^2). Similarly divide (x^3 - y^3) by (x - y) and get (x^2 + xy + y^2)

If you are a student and wish to learn this I suggest that you learn the
pattern:

(x^3 + y^3) = (cube root of x^3 + cube root of y^3)((cube root of x^3)^2 -
product of the two cube roots + (cube root of y^3)^2)

For example:

(64 - 27x^6) = (4 - 3x^2)(16 + 12x^2 + 9x^4)

Practice some.

Marielouise, for the Teacher2Teacher service

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