What is the Fully Factored Form of 32a3 12a2?

Learn how to find the fully factored form of 32a3 12a2 with our comprehensive guide. Simplify complex equations and boost your algebra skills today!

Introduction

When it comes to understanding mathematical expressions, there are certain terms and phrases that can be confusing. One such term is the “fully factored form.” This term is often used in algebra to describe a particular way of expressing an equation. If you’re struggling to understand what the fully factored form is, don’t worry! In this article, we’ll explore this term in more detail and discuss how it applies to the equation 32a3 12a2.

What is Factoring?

Before we dive into the fully factored form, let’s first define what factoring is. Factoring is the process of breaking down a mathematical expression into its constituent parts. For example, if we have the equation x2 + 5x + 6, we can factor it into (x + 2)(x + 3). Factoring can be a useful tool in algebra, as it can help to simplify complex equations and make them easier to work with.

One type of factoring that is particularly useful is called “common factoring.” Common factoring involves finding the largest common factor that two or more terms in an equation share and then factoring it out. For example, in the equation 6×2 + 9x, we can factor out 3x to get 3x(2x + 3). This makes the equation easier to work with as we can now focus on the remaining terms.

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What is the Fully Factored Form?

Now that we have an understanding of what factoring is let’s move on to the fully factored form. The fully factored form is the expression of an equation in which all of its factors are written out completely. This means that there are no more common factors that can be factored out. The fully factored form is often used in algebra as it provides a simplified expression of an equation that is easy to work with.

When we factor an equation, we often end up with multiple expressions that are multiplied together. For example, in the equation 2×2 + 6x + 4, we can factor out 2 to get 2(x2 + 3x + 2). We can then further factor the expression inside the parentheses to get 2(x + 1)(x + 2). This is the fully factored form of the equation.

Factor the Equation

Let’s move on to the equation we’re trying to find the fully factored form of: 32a3 12a2. To factor this equation, we need to find the largest common factor that the two terms share. In this case, the largest common factor is 4a2. We can factor it out to get 4a2(8a + 3).

So, the fully factored form of 32a3 12a2 is 4a2(8a + 3). This expression is fully factored because we can’t factor it any further. It is a simplified version of the original equation that is easier to work with.

Simplify the Equation

Now that we have the fully factored form of the equation, we can simplify it further. One way to do this is to distribute the 4a2 term to the expression inside the parentheses. Doing so gives us:

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4a2(8a + 3) = 32a3 + 12a2

As you can see, we have arrived back at the original equation! However, we now have a better understanding of how it can be factored and simplified.

Simplifying equations can be helpful in a variety of situations. For example, it can make it easier to solve equations, compare expressions, or find patterns. In this case, simplifying the equation allowed us to confirm that we had found the correct fully factored form.

Conclusion

In conclusion, the fully factored form is an expression of an equation in which all of its factors are written out completely. Factoring can be a helpful tool in algebra, as it can simplify complex equations and make them easier to work with. By factoring the equation 32a3 12a2, we found its fully factored form to be 4a2(8a + 3). We then simplified the equation to arrive back at the original expression. Hopefully, this article has helped to clarify what the fully factored form is and how it can be used in algebra.

Simplify the Equation

Now that we have factored the equation 32a3 12a2, let’s simplify it further to arrive at its fully factored form.

First, let’s factor out the greatest common factor, which is 4a2. This gives us:

4a2(8a + 3)

We can see that there are no more common factors that can be factored out, so this is the fully factored form of the equation.

Conclusion

In conclusion, the fully factored form of 32a3 12a2 is 4a2(8a + 3). Factoring an equation can be a useful tool in algebra, as it can help to simplify complex expressions and make them easier to work with. The fully factored form provides a simplified expression of an equation that is easy to understand and work with. By understanding the fully factored form, you can improve your algebra skills and tackle more complex mathematical problems.

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