How Do I Factorize Odd Exponents?

Question

for example: (a^3-b^3)

how would i factorize that?

thanks.

Answer 1

You can factor a^3 - b^3 using this formula:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

(The person who called this a "difference in squares" is wrong.  It's the difference of two CUBES.)

Similarly:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

When it comes to other cubic expressions though, like "x^3 + x^2 - 3x + 1", then it gets tricky.  You typically have to use something like polynomial division.

Answer 2

This is called a difference of squares: (a-b)(a^2+ab+b^2)

Answer 3

(a-b)(a^2+ab+b^2)

This is one most people just memorize, also the sum of two cubes, you can get them online here: http://www.math.unt.edu/mathlab/emathlab...

Answer 4

Ok, well first, I like to factor out the GCF.

The GCF is a-b... However, it is not a^2-b^2

Now there is a process that you can do:

(a-b)(a^2+ab+b^2)

That's the answer... But this is the formula:

Put the GCF in front (a-b) multiply that by a^2 - a times b + b^2....

For example if you had to factor this: 8x^3-1... The GCF is 2x-1 because... 2^3=8 x^3=x^3 and -1^3=-1...

So you multiply (2x-1) by a^2-ab+b^2....

(2x-1)(4x^2+2x+1)... We can check all of this multiplying these two terms....

8x^3 is the result when we multiply these two terms...

(a-b)(a^2+ab+b^2)

Good luck.