Math CentralQuandaries & Queries


Question from Amanda, a student:

It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2]-[1/x+2]. Please help!!!

Hi Amanda,

The expressions for factoring the sum and difference of cubes are

x3 + y3 = (x + y)(x2 - xy + y2)
x3 - y3 = (x - y)(x2 + xy + y2)

If you add or subtract algebraic fractions you need to find a common denominator just as in adding or subtracting numerical fractions. For your example


a common denominator is (x + h + 2)(x + 2). Thus multiply the numerator and denominator of the first fraction by x + 2 and the numerator and denominator of the second fraction by x + h + 2. This gives


Now that the fractions have the same denominator you can subtract the numerators


I hope this helps,

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS