Greetings math friends! This post will go over expanding cubed binomials using two different methods to get the same answer. Weβre so used to seeing squared binomials such as, , and expanding them without a second thought. But what happens when our reliable squared binomials are now raised to the third power, such as,? Luckily for us, there is a **Rule** we can use:

But where did this rule come from? And how can we so blindly trust it? In this post we will **prove** why the above rule works for expanding cubed binomials using 2 different methods:

**Why bother? **Proving this rule will allow us to expand and simplify any cubic binomial given to us in the future! And since we are proving it 2 different ways, you can choose the method that best works for you.

**Method #1**: **The Box Method**

**Step 1: **First, focus on the left side of the equation by expanding (a+b)^{3}:

**Step 2: **Now we are going to create our first box, multiplying (a+b)(a+b). Notice we put each term of (a+b) on either side of the box. Then multiplied each term where they meet.

**Step 3:** Combine like terms **ab** and **ab**, then add each term together to get a^{2}+2ab+b^{2}.

**Step 4:** Multiply (a^{2}+2ab+b^{2})(a+b) making a bigger box to include each term.

**Step 5: **Now combine like terms (**2a ^{2}b** and

**a**) and (

^{2}b**2ab**and

^{2}**ab**), then add each term together and get our answer: a

^{2}^{3}+3a

^{2}b+3ab

^{2}+b

^{3}.

**Method #**2: **The Distribution Method**

Let’s expand the cubed binomial using the distribution method step by step below:

Now that weβve gone over 2 different methods of cubic binomial expansion, try the following practice questions on your own using your favorite method!

**Practice Questions:** Expand and simplify the following.

**Solutions:**

Still, got questions? No problem! Check out the video above or comment below! Happy calculating! π

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****Bonus**: Test your skills with this ** Regents question **on Binomial Cubic Expansion!