Combining like terms worksheet answers play a crucial role in simplifying algebraic expressions. By understanding the concept and techniques involved, students can effectively solve equations, manipulate polynomials, and tackle various mathematical problems.

This comprehensive guide delves into the intricacies of combining like terms, exploring both positive and negative coefficients, and highlighting the significance of the distributive property in this process.

Combining Like Terms

Combining like terms is a fundamental operation in algebra that involves grouping terms with the same variable and exponent. This process simplifies algebraic expressions and makes them easier to solve.

Types of Like Terms

Like terms can be classified into two types:

• Numerical coefficients:Terms with the same numerical coefficient, such as 5x and 3x.
• Variables:Terms with the same variables raised to the same exponent, such as x ²and 2x ².

Combining Like Terms with Positive Coefficients

To combine like terms with positive coefficients, simply add the coefficients and keep the same variable and exponent.

Example:

Combine 5x + 3x

Solution:

5x + 3x = 8x

Combining Like Terms with Negative Coefficients

To combine like terms with negative coefficients, subtract the absolute values of the coefficients and keep the same variable and exponent. The resulting coefficient will have the sign of the term with the larger absolute value.

Example:

Combine 5x – 3x

Solution:

5x – 3x = 2x

Distributive Property and Combining Like Terms

The distributive property can be used to combine like terms by multiplying the common factor by each term in the parentheses.

Example:

Combine 2(x + 3)

Solution:

2(x + 3) = 2x + 2(3) = 2x + 6

Applications of Combining Like Terms, Combining like terms worksheet answers

Combining like terms is used in various fields, including:

• Algebra:Simplifying algebraic expressions, solving equations, and factoring polynomials.
• Physics:Combining forces and velocities in vector calculations.
• Economics:Combining terms in economic models to represent supply and demand.

Common Mistakes in Combining Like Terms

Common mistakes include:

• Adding or subtracting variables instead of coefficients.
• Changing the exponent when combining terms with different exponents.
• Ignoring the signs of the coefficients.

Worksheets and Practice

Worksheet:

Combine the following like terms:

1. 5x + 3x
2. 2y
   

   4y

3. 3x ²+ 2x ²
4. 4(x + 2)

Answer Key:

1. 8x
2. -2y
3. 5x²
4. 4x + 8

FAQ Section: Combining Like Terms Worksheet Answers

What is the significance of combining like terms?

Combining like terms simplifies algebraic expressions, making them easier to solve and manipulate.

How do you combine like terms with positive coefficients?

Add the coefficients of like terms while retaining the variable part.

What is the distributive property and how does it relate to combining like terms?

The distributive property allows you to multiply a sum or difference by a factor and then combine like terms.