An Intro to Combining Like Terms | Simplifying Expressions by Combining Like Terms | Math with Mr. J

Summary

In this video, Mr. J introduces the concept of combining like terms in algebraic expressions. He explains that like terms have the same variables raised to the same power and shows how to simplify expressions by adding or subtracting the coefficients of these terms. Using examples, such as 9x + 3x and more complex expressions, Mr. J guides viewers through the process of identifying and combining like terms to make algebraic expressions simpler and easier to work with. This video is a step-by-step introduction for students learning to streamline their algebraic equations.

Takeaways

• 🧮 Combining like terms helps simplify algebraic expressions.
• 📚 Like terms are terms that have the same variables raised to the same powers.
• ➕ When combining like terms, you only add or subtract the coefficients of the terms.
• 🔢 In expressions without visible exponents, the exponent is understood to be 1.
• ✏️ To simplify expressions, look for terms with the same variables and powers, then combine them.
• 💡 It's helpful to rearrange terms with the same variables next to each other to make combining easier.
• 🔄 You can rewrite expressions with addition instead of subtraction to simplify identification of negative terms.
• ✔️ Example 1: 9x + 3x simplifies to 12x by adding coefficients (9 + 3).
• ✔️ Example 2: 8G + 5G + 7 + 2 simplifies to 13G + 9 by combining G terms and constants.
• 🔀 Rearranging and rewriting expressions can help in organizing terms before combining like terms.

Q & A

What are like terms in algebraic expressions?

Like terms are terms that have the same variables raised to the same powers. Only these terms can be combined in an algebraic expression.

Why is it important to combine like terms?

Combining like terms simplifies an algebraic expression, making it easier to understand and work with while retaining its original value.

In the expression 9x + 3x, why are the terms considered like terms?

Both terms have the same variable, 'x', and the exponent of the variable is the same (in this case, 1), which makes them like terms.

How do you combine like terms in an expression?

To combine like terms, you simply add or subtract the coefficients (the numerical part) of the terms while keeping the variable and its exponent unchanged.

What is the simplified form of the expression 9x + 3x?

The simplified form of 9x + 3x is 12x, since 9 + 3 equals 12, and the variable 'x' remains unchanged.

How would you simplify the expression 8G + 7 + 5G + 2?

First, combine the like terms 8G and 5G to get 13G, and then combine the constants 7 and 2 to get 9. The simplified expression is 13G + 9.

What strategy does the speaker suggest for simplifying more complex expressions?

The speaker suggests rearranging and rewriting the expression so that like terms are placed next to each other. This makes it easier to identify and combine them.

Why is there an 'understood' exponent of 1 in expressions like 9x or 3x?

When there is no exponent written, it is understood that the variable is raised to the power of 1, because any number or variable raised to the power of 1 equals itself.

How can you simplify the expression 6y² + 10y + 2y² + 3y + y?

First, combine the like terms for y²: 6y² + 2y² = 8y². Then combine the like terms for y: 10y + 3y + 1y = 14y. The simplified expression is 8y² + 14y.

What is the advantage of rewriting subtraction as adding the opposite when simplifying expressions?

Rewriting subtraction as adding the opposite helps organize the expression, making it easier to identify negative terms and combine like terms more accurately.