Learning Objectives:

__Math Tutoring on Factoring a Sum or Difference of Cubes__

The **sum or difference of two cubes** can be **factored** into a product of binomial times a trinomial. That is, **x³+y³=(x+y)(x²−xy+y²) **and** x³−y³=(x−y)(x²+xy+y²).** A mnemonic for the signs of the **factorization** is the word **"SOAP",** the letters stand for **"Same sign"** as in the middle of the original expression, **"Opposite sign",** and **"Always Positive".**

That is **x³±y³=(x[Same sign]y)(x²[Opposite sign]xy[Always Positive]y²)**

Here are the steps required for **factoring a sum of cubes **which is followed** **in math tutoring**:**

**Step 1: **Decide if the two terms have anything in common, called the **greatest common factor or GCF.** If so, **factor** out the **GCF.** Do not forget to include the **GCF** as part of your final answer.

**Step 2:** Rewrite the original problem as a **difference of two perfect cubes.**

**Step 3:** Use the following sayings to help write the answer: **“Write What You See”, “Square-Multiply-Square” “Same, Different, End on a Positive”**

**Step 4:** Use these three pieces to write the final answer.

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**Hook Questions:**

*1. **What is factoring the sum and difference of two cubes?*

*2. **How do you factor perfect cubes?*

*3. **How do you factor a cubic binomial?*

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