Combine Any Like Terms In The Expression. If There Are No Like Terms, Rewrite The Expression.$\[ 16z^2 + 11z^2 + Z^2 - 28z^2 \\]

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable and exponent. In this article, we will explore how to combine like terms in an algebraic expression and provide examples to illustrate the concept.

What are Like Terms?

Like terms are terms that have the same variable and exponent. For example, in the expression $2x^2 + 3x^2$, the terms $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ and the exponent $2$. On the other hand, the terms $2x^2$ and $3x$ are not like terms because they have different exponents.

Combining Like Terms

To combine like terms, we simply add or subtract the coefficients of the like terms. For example, in the expression $2x^2 + 3x^2$, we can combine the like terms by adding the coefficients:

$$2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$$

Similarly, if we have an expression with negative coefficients, we can combine the like terms by subtracting the coefficients:

$$-2x^2 + 3x^2 = (-2 + 3)x^2 = x^2$$

Example 1: Combining Like Terms

Let's consider the expression $16z^2 + 11z^2 + z^2 - 28z^2$. To simplify this expression, we need to combine the like terms.

$$16z^2 + 11z^2 + z^2 - 28z^2$$

We can start by combining the like terms $16z^2$ and $11z^2$:

$$16z^2 + 11z^2 = (16 + 11)z^2 = 27z^2$$

Next, we can combine the like terms $27z^2$ and $z^2$:

$$27z^2 + z^2 = (27 + 1)z^2 = 28z^2$$

Finally, we can combine the like terms $28z^2$ and $-28z^2$:

$$28z^2 - 28z^2 = (28 - 28)z^2 = 0$$

Therefore, the simplified expression is:

$$0$$

Example 2: Combining Like Terms with Negative Coefficients

Let's consider the expression $-3x^2 + 2x^2 - 4x^2$. To simplify this expression, we need to combine the like terms.

$$-3x^2 + 2x^2 - 4x^2$$

We can start by combining the like terms $-3x^2$ and $2x^2$:

$$-3x^2 + 2x^2 = (-3 + 2)x^2 = -x^2$$

Next, we can combine the like terms $-x^2$ and $-4x^2$:

$$-x^2 - 4x^2 = (-1 - 4)x^2 = -5x^2$$

Therefore, the simplified expression is:

$$-5x^2$$

Conclusion

Combining like terms is an essential concept in algebra that helps simplify complex expressions. By identifying and combining like terms, we can simplify expressions and make them easier to work with. In this article, we have explored how to combine like terms and provided examples to illustrate the concept.

Tips and Tricks

• Always start by identifying the like terms in an expression.
• Combine the like terms by adding or subtracting the coefficients.
• Make sure to simplify the expression by combining all the like terms.
• Use parentheses to group the like terms and make it easier to combine them.

Practice Problems

1. Simplify the expression $4x^2 + 2x^2 - 3x^2$.
2. Simplify the expression $-2x^2 + 3x^2 - 4x^2$.
3. Simplify the expression $16z^2 + 11z^2 + z^2 - 28z^2$.

Answer Key

1. $3x^2$
2. $-3x^2$
3. $0$
   Combining Like Terms: Frequently Asked Questions =====================================================

Introduction

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. In this article, we will answer some frequently asked questions about combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, in the expression $2x^2 + 3x^2$, the terms $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

Q: How do I combine like terms?

A: To combine like terms, you simply add or subtract the coefficients of the like terms. For example, in the expression $2x^2 + 3x^2$, you can combine the like terms by adding the coefficients:

$$2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$$

Q: What if I have an expression with negative coefficients?

A: If you have an expression with negative coefficients, you can combine the like terms by subtracting the coefficients. For example, in the expression $-2x^2 + 3x^2$, you can combine the like terms by subtracting the coefficients:

$$-2x^2 + 3x^2 = (-2 + 3)x^2 = x^2$$

Q: Can I combine like terms with different variables?

A: No, you cannot combine like terms with different variables. For example, in the expression $2x^2 + 3y^2$, you cannot combine the like terms because they have different variables.

Q: What if I have an expression with multiple like terms?

A: If you have an expression with multiple like terms, you can combine them by adding or subtracting the coefficients. For example, in the expression $2x^2 + 3x^2 + 4x^2$, you can combine the like terms by adding the coefficients:

$$2x^2 + 3x^2 + 4x^2 = (2 + 3 + 4)x^2 = 9x^2$$

Q: Can I simplify an expression by combining like terms?

A: Yes, you can simplify an expression by combining like terms. For example, in the expression $16z^2 + 11z^2 + z^2 - 28z^2$, you can combine the like terms to simplify the expression:

$$16z^2 + 11z^2 + z^2 - 28z^2 = 0$$

Q: What if I have an expression with no like terms?

A: If you have an expression with no like terms, you cannot simplify the expression by combining like terms. For example, in the expression $2x^2 + 3y^2$, you cannot combine the like terms because they have different variables.

Conclusion

Combining like terms is an essential concept in algebra that helps simplify complex expressions. By understanding how to combine like terms, you can simplify expressions and make them easier to work with. In this article, we have answered some frequently asked questions about combining like terms.

Tips and Tricks

• Always start by identifying the like terms in an expression.
• Combine the like terms by adding or subtracting the coefficients.
• Make sure to simplify the expression by combining all the like terms.
• Use parentheses to group the like terms and make it easier to combine them.

Practice Problems

1. Simplify the expression $4x^2 + 2x^2 - 3x^2$.
2. Simplify the expression $-2x^2 + 3x^2 - 4x^2$.
3. Simplify the expression $16z^2 + 11z^2 + z^2 - 28z^2$.

Answer Key

1. $3x^2$
2. $-3x^2$
3. $0$