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Factoring the Sum and Difference of Two Squares or Two Cubes

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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.

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