# Difference between revisions of "Sum and difference of powers"

m (LaTeX) |
m |
||

Line 42: | Line 42: | ||

<math>(p+1)y^p\leq (y+1)^{p+1}-y^{p+1}\leq (p+1)(y+1)^p</math> | <math>(p+1)y^p\leq (y+1)^{p+1}-y^{p+1}\leq (p+1)(y+1)^p</math> | ||

+ | |||

+ | ==Sum of Cubes== | ||

+ | <math>1^3=1^2</math> | ||

+ | |||

+ | <math>1^3+2^3 =3^2</math> | ||

+ | |||

+ | <math>1^3 +2^3+3^3=6^2</math> | ||

+ | |||

==See Also== | ==See Also== |

## Revision as of 11:08, 6 April 2016

The **sum and difference of powers** are powerful factoring techniques that, respectively, factor a sum or a difference of certain powers.

## Sums of Powers

## Differences of Powers

If is a positive integer and and are real numbers,

For example:

Note that the number of terms in the *long* factor is equal to the exponent in the expression being factored.

An amazing thing happens when and differ by , say, . Then and

.

For example:

If we also know that then:

## Sum of Cubes

## See Also

- Factoring
- Difference of squares, an extremely common specific case of this.

*This article is a stub. Help us out by expanding it.*