# Shaking the Cubes

Topic:
Algebra, Cube

## OBJECTIVE: To learn how to factor the sum and difference of two cubes

In a previous lesson, you learned how to factor the first of three special binomials—the Difference of Two Squares. Betting on Squares: https://www.geogebra.org/m/d4jth98g In this lesson, you'll learn how to factor the two remaining special binomials: Sum of Two Cubes and Difference of Two Cubes. You've been told before that there's no such thing as Sum of Two Squares. Well ... there is ... x² + y² ... but it cannot be factored, and we say it's 'prime.' But in the case of cubes, we can factor both the sum and the difference. Here are the formulas: Sum of Two Cubes : x³ + y³ = (x + y)(x² - xy + y²) Difference of Two Cubes : x³ - y³ = (x - y)(x² + xy + y²) Notice how the two formulas are very much alike? In fact, you can just memorize one formula, and just remember what switches you have to make to come up with the other formula. Here's how it works: Remember that there are two factors—a binomial and a trinomial. To obtain the terms of the binomial factor, get the cube roots of the two terms of the original problem and connect them with the same sign (plus for sum and minus for difference). The three terms of the trinomial factor are obtained from the two terms of the binomial factor, as follows: square the first term, then multiply the two terms and switch the sign, and finally square the second term. There!

## Illustrations:

Below is a set of problems that require you to factor the Sum or Difference of Two Cubes. Check the Answer Box below for the correct answers.

Check out the answers to the above problems here.

## TODAY you learned how to factor the Sum and Difference of Two Cubes.

In future lessons, you'll learn how to factor trinomials. Did you have FUN in today's activities?