# What is a Cubic Binomial and How To Solve It Simply

Have your kids come home with a math problem to solve for the next day?

Is it a cubic binomial? Now, you’re probably browsing the little knowledge you have left from when you attended school. You surely want to look good in front of your kids and help them solve it. Well, you don’t need to have a maths degree or to be a maths teacher to help them!

You’ll undoubtedly impress your kids with your knowledge and patience. Your kids might even impress your teacher with what you taught them! All you need to do is read and follow along with this comprehensive step-to-step guide.

## What Is A Monomial?

A monomial is a mathematical expression with only one term. It includes whole numbers, numbers, and variables that are multiplied between each other. For example, 7c is a monomial.

All numbers are monomials, as a monomial is when a number is raised to the first power. As every number raised to the first power is equal to itself, all numbers are therefore monomials.

So that means that 7c^1 = 7c

## What Is A Binomial?

That’s one of the first questions you need to answer to explain the concept to your kids.
A binomial is a fundamental part of algebra, and it’s much easier than it looks. It’s simply a mathematical expression with only two terms.

So to first identify that you are in front of a binomial, here is an example of what it can look like: c+ 7

## What Is A Cubic Binomial?

So what is a cubic binomial, and what does it look like?

A cubic binomial is when at least one of the variables of the equation is raised to the third power. Or, in other words, it’s when at least one variable of the equation is cubed (so multiplied by itself three times).

This is why it’s called a cubic binomial. It’s also a type of polynomial.

So, either one or two of the terms from the binomial are raised to the third power. So if you take our formula from earlier, here’s what it could look like: c^3 +7

Often, binomials contain variables raised to other powers. For example, c^3 +c^2
Despite the fact that this last formula contains a quadratic (c^2), the first term makes it a cubic binomial (c^3). The formula gets its name from the highest power of any variable.

For example, if this formula were actually c^4 + c^3, then the highest power would be c^4, and this would no longer be a cubic binomial and would be a quartic binomial.

This might be complicated at first, but I promise you’ll get the hang of it quickly!

## What Is A Polynomial?

A cubic binomial is a type of polynomial. But what is a polynomial?

A polynomial is any formula that contains multiple terms. The easy way to remember this is to keep in mind the meaning of the actual word: ‘poly’ means multiple in Greek, and ‘nomen’ meaning term or name in Latin. Therefore, the name itself means multiple terms.

Here is an example of a polynomial: c^2 + c + 7

So a cubic binomial is a polynomial that is binomial and cubic.

## How Do You Simplify A Cubic Binomial?

If your kid’s homework is to simplify a cubic binomial, there are multiple ways to do it.

### Identifying The Situation To Simplify A Cubic Binomial

There are various situations that it could refer to:

1) It could be that a single term from the binomial like (c + 3) is raised to the third power.

2) It could be that every term from the binomial is individually cubed (c^3 + d^3).

3) It could be that only one term is raised to the third power, while the other term is either just a normal number (not a variable) or is a variable raised to a power less than 3—for example, c^3 – c^2.

You can apply a formula to the first two situations, while the third one uses another method.

### Methods To Simplify A Cubic Binomial

So how do you solve a cubic binomial? There are shortcut formulas for special cases.

1. If your cubic binomial is a sum, use this equation formula:

(u+i)^3
=(u+i)x(u+i)x(u+i)
=u^3+i^3+3u^2i+3ui^2

2. If your cubic binomial is a difference, use this equation formula:

(u-i)^3
=(u-i)x(u-i)x(u-i)
=u^3-i^3-3u^2i+3ui^2

3. If your cubic binomial is a sum of cubes, use this equation formula:

u^3 + i^3
=(u+i) x (u^2 = i^2-iu)

4. If your cubic binomial is the difference of cubes, use this equation formula:

u^3-i^3
=(u-i)x(u^2+i^2+iu)

5. If your cubic binomial is any other, you can’t simplify a cubic binomial. This has one exception, though: when both terms of the cubic binomial have the exact same variable, you can factor out that number of term.
6.
So if it’s c^3 + c^2, you can factor the lowest term out of the equation. So, for example:

3d3 -6d2
=3d2(d-2)

## How Do You Cube A Binomial?

If your kid’s homework requires to cube a binomial, that’s simple to solve. If you want to cube a binomial, you have to expand the equation. If the equation is (c+7)^3, it’s the equivalent of (c+7) x (c+7)x (c+7). See? It’s really that simple!

If you want to then expand this, you need to multiply it out.
=(c^2+14c+49)*(c+7)

Here are some other examples so you can really grasp the concept:

=c^3+3c^2+3c+1
=(c^2+2c+1)(c+1)
=(c+1)(c+1)(c+1)
=(c+1)^3

=c^3+-2c^2+3c-1
=(c^2-2c+1)(c-1)
=(c-1)(c-1)(c-1)
=(c-1)^3

9c^3-3c
=3c(3c^2-1)

c^3d^3+d^2
=d^2(c^3d+1)

## Final Thoughts

So there you go, now you know everything about cubic binomials and how to solve them! Your kids will definitely be impressed with your extensive knowledge of each. And you’ll be able to them that, after all, maths isn’t that difficult!

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