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can you multiply like terms ?

### Can You Multiply Like Terms?

When working with algebra, the concept of like terms is fundamental – not just for addition and subtraction, but also for multiplication and division. Like terms are terms that contain the same variables raised to the same power. These terms can be manipulated in several ways, including multiplication, which is the subject of this post.

#### What Does it Mean to Multiply Like Terms?

Multiplying like terms is a straightforward process, particularly when you understand how to handle the coefficients (the numerical parts of the terms) and the variables. When you multiply like terms, you follow two primary steps:

1. **Multiplication of Coefficients:** Just as you would multiply any two numbers, you multiply the coefficients of your like terms.
2. **Addition of Exponents:** For the variables, if they have exponents, you add the exponents if the terms are like terms (having the same base and same variables).

#### Example of Multiplication

Let’s consider multiplying two like terms, say 3x² and 4x². The process would be as follows:

1. **Multiplication of Coefficients:** Multiply the coefficients 3 and 4, which gives you 12.
2. **Addition of Exponents:** Since the terms have the same base (x), and the exponents are both 2, adding the exponents is not necessary in this direct multiplication, but when multiplying two terms with different exponents (assuming like terms), you would add the exponents.

So the multiplication of 3x² by 4x² would give us 12x² since the exponents are the same.

#### Division of Like Terms

It’s worth noting that the division of like terms follows a similar logic in terms of handling the coefficients and the base. When dividing, you essentially reverse the addition of the exponents in multiplication, which means you subtract the exponents of like terms.

#### Importance and Applications

The ability to multiply and divide like terms is extremely important when simplifying algebraic expressions or solving equations. Mastery of this skill ensures that you can navigate more complex algebraic processes with ease.

#### Educational Resources

For further learning or a more in-depth tutorial on multiplying and dividing like terms, several resources provide comprehensive guidelines and examples:

– **Krista King Math Blog:** Offers detailed explanations and examples on how to handle multiplication and division of like terms.
– **YouTube:** There are several videos, such as the ones by “KristaKingMath” or other educational channels, which offer visual walkthroughs and examples to help grasp these concepts.
– **Khan Academy:** Provides both practice exercises and instructional videos on manipulating like terms, including multiplication, division, and combining like terms overall.

Understanding these operations on like terms not only sharpens your algebra skills but also serves as a foundational skill for more advanced mathematical techniques and concepts.

If you’re ready to dive deeper into the essence and mechanics of these terms in algebra, following the references and links provided can be invaluable. So, let’s multiply knowledge by diving into the fascinating world of algebraic terms, one like term multiplication at a time!