Factoring the Sum and Difference of Two Squares or Two Cubes
When we talk about the "sum of two squares" or "the difference of two cubes", what we mean is a binomial that can be written as something squared (cubed) plus or minus something else squared (cubed). For example,
$$x^2 + 16$$can be written as
$$x^2 + 4^2$$Notice how both terms are something squared - x in the first term and 4 in the second. This is the pattern that we're looking for use this factoring method.
Once you've rewritten a polynomial this way, doing the actual factoring is just using a formula.
| Difference of Two Squares: | $a^2 - b^2 = (a + b)(a - b)$ |
| Sum of Two Squares: | prime / can't be factored |
| Difference of Two Cubes: | $a^3 - b^3 = (a + b)(a^2 + ab + b^2)$ |
| Sum of Two Cubes: | $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ |
At first glance, the formulas, especially the cube ones, look a little messay so we'll go over several examples in the videos.
Video Lectures
Binomials are a special case in factoring. In this lecture, we're going to look at the method for factoring a binomial that's the sum/difference of two squares.
In this lecture, we're going to look at the second special class of factorable binomials - the sum/difference of two cubes.
