My name is Melissa and I am a student.

I would like you to help me factor (x 6-y 6) & (a+b)2+3(a+b)-4

Thank You

Hi Melissa,

A large part of algebra is recognizing patterns. Much like hearing the first bar of a song and recognizing that it's Metallica playing ... or looking at a diagram and seeing part of it as a right triangle.

For your first problem (x 6-y 6) the key is to see it, not as a difference of two sixths powers but as a difference of two squares. That is to see it as

((x3)2 - (y3)2)
(p2 - q2)

where p = x3 and q = y3

Factor this as a difference of squares and you will have two factors, one which is a difference of cubes and the other a sum of cubes. These you should also recognize and be able to factor.

Your second problem,


is similar in that you need to see the pattern


where x = a+b. Factor x2+3x-4 and substitute a+b for x.

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