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

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

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.