Skills:

Factor and Solve polynomials by applying Sum and Difference of Cubes
Review of Factoring (and Solving) polynomials in Quadratic Form

Sum and Difference of Cubes

Factoring Sum and Difference of Cubes requires knowing these two formulas:

$LaTeX: a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$

$LaTeX: a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$

Here is a video of a teacher doing a few examples with these formulas:

Factoring Sums and Differences of Cubes

Notice that the video explains how to factor, not necessarily how to solve. Think about how you can apply your knowledge of solving from the quadratics unit in this situation.

Quadratic Form (special case): Difference of Quartics (a type of quadratic form)

You can factor binomials in the form LaTeX: a^4-b^4 by using the difference of squares from the quadratics unit. Remember the Difference of Squares formula is $LaTeX: a^2-b^2=\left(a-b\right)\left(a+b\right)$ .

This means $LaTeX: a^4-b^4\:=\left(a^2\:-\:b^2\right)\left(a^2+\:b^2\right)\:which\:can\:be\:factored\:further\:to\:\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right).$

Quadratic Form:

We can use our tools for factoring and solving quadratics to polynomials of higher degree in the form:

$LaTeX: ax^{2n}+bx^n+c$

Notice how the exponents in these polynomials follow a pattern. Here is a video that explains how to factor quartic polynomials.

https://youtu.be/9G5hfxUxWE4

Again, use your skills to solve a factored quadratic equation from the past lessons to extend these factoring techniques into solving techniques.

If you would rather read about these techniques, please visit these websites for reference:

http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/sum_of_cubes/sum_of_cubes.html

https://www.ck12.org/book/ck-12-algebra-ii-with-trigonometry-concepts/section/6.8/