How to Add and Subtract Terms with variables

Hello! Today, we are going to learn about adding and subtracting terms that contain variables. This is an important skill in algebra that will help you solve many types of math problems. Let’s dive in and make it fun and easy to understand!

What Does It Mean to Add and Subtract Terms?

When we add or subtract terms, we combine or separate them. But there’s a rule: we can only add or subtract like-terms. Like terms are terms that have the same variable raised to the same power.

Examples of Like-Terms:

• $2x$ and $5x$ (both have the variable $x$)
• 3y² and −7y² (both have the variable y²)

Examples of Unlike Terms:

• $4x$ and $3y$ (different variables)
• $2x$ and 2x² (same variable, different powers)

How to Add Like-Terms

Let’s look at an example of adding like terms.

Example 1:

Expression: $2x+3x$

Steps to Add:

1. Identify the like terms. Here, both terms have the variable $x$.
2. Add the coefficients (the numbers in front of the variables):
   $$2+3=5$$
3. Combine the terms:
   $$2x+3x=5x$$

Answer: $5x$

Example 2:

Expression: $4y+7y-2y$

Steps to Add:

1. Identify the like-terms. Here, all terms have the variable $y$.
2. Add the coefficients:
   $$4+7-2=9$$
3. Combine the terms:
   $$4y+7y-2y=9y$$

Answer: $9y$

How to Subtract Like-Terms

Now let’s look at an example of subtracting like-terms.

Example 3:

Expression: $6a-4a$

Steps to Subtract:

1. Identify the like-terms. Here, both terms have the variable $a$.
2. Subtract the coefficients:
   $$6-4=2$$
3. Combine the terms:
   $$6a-4a=2a$$

Answer: $2a$

Example 4:

Expression: $10b-3b-2b$

Steps to Subtract:

1. Identify the like-terms. Here, all terms have the variable $b$.
2. Subtract the coefficients:
   $$10-3-2=5$$
3. Combine the terms:
   $$10b-3b-2b=5b$$

Answer: $5b$

Practice Problems

Let’s practice adding and subtracting terms with variables.

Problem 1: $3x+4x$

Steps to Solve:

1. Identify like terms: $3x$ and $4x$.
2. Add the coefficients:
   $$3+4=7$$
3. Combine the terms:
   $$3x+4x=7x$$

Answer: $7x$

Problem 2: $5y-2y+y$

Steps to Solve:

1. Identify like terms: $5y$, $-2y$, and $y$.
2. Combine the coefficients:
   $$5-2+1=4$$
3. Combine the terms:
   $$5y-2y+y=4y$$

Answer: $4y$

Problem 3: $8a-3a+2a$

Steps to Solve:

1. Identify like terms: $8a$, $-3a$, and $2a$.
2. Combine the coefficients:
   $$8-3+2=7$$
3. Combine the terms:
   $$8a-3a+2a=7a$$

Answer: $7a$

Problem 4: t + 5 – 8t  – 4 – 2t

Steps to Solve:

1. Identify like terms:
   • t, $-8t$, and -2t$are\; like-terms.$
   • 5 and -4 are like-terms.
2. Arrange the like-terms in given expression:
   • t – 8t – 2t + 5 – 4
3. Answer the like-terms:
   • $$t\; –\; 8t\; –\; 2t\; =\; –\; 9t$$
   • 5 – 4 = 1
4. Add answers of like-terms to determine final answer.
   • t – 8t – 2t + 5 – 4 = – 9t + 1

Answer: – 9t + 1

Problem 5: y² + 3y – 4x – y² – 8x + 5

Steps to Solve:

1. Identify like-terms:
   • y² and – y² are like-terms.
   • – 4x and – 8x are like-terms
   • 3y and 5 do not have any like-term.
2. Arrange the like-terms in given expression:
   • y² – y² – 4x – 8x + 3y + 5
3. Answer the like-terms:
   • $$y²\; –\; y²\; =\; 0$$
   • – 4x – 8x = – 12x
4. Add answers of like-terms to determine final answer.
   • y² – y² – 4x – 8x + 3y + 5 = 0 – 12x + 3y + 5

Answer: – 12x + 3y + 5

Problem 6: y² + 3y – 4x – y² – 8x + 5

Steps to Solve:

1. Identify like-terms:
   • y² and – y² are like-terms.- 4x and – 8x are like-terms3y and 5 do not have any like-term.
2. Arrange the like-terms in given expression:
   • y² – y² – 4x – 8x + 3y + 5
3. Answer the like-terms:
   • $$y²\; –\; y²\; =\; 0$$
   • – 4x – 8x = – 12x
4. Add answers of like-terms to determine final answer.
   • y² – y² – 4x – 8x + 3y + 5 = 0 -12x + 3y + 5

Answer: -12x + 3y + 5

Problem 7: xy² + 4y – 2x – x²y + 5

Steps to Solve:

1. Identify like-terms:
   • None of these terms are like-terms.

So, this expression cannot be simplified.

Answer: xy² + 4y – 2x – x²y + 5

Common Questions and Misconceptions

Q: Can I add or subtract terms with different variables?

A: No, you can only add or subtract like-terms, which are terms with the same variable and the same power.

Q: What if the coefficients are negative?

A: You handle negative coefficients the same way you handle positive ones. Just follow the rules for adding and subtracting negative numbers.

Q: Can terms without variables be added to terms with variables?

A: No, terms without variables (constants) cannot be added to terms with variables. They are not like-terms.

Ask Question:

• • If you’re stuck, don’t hesitate to ask any question in the Comment Section below.

Conclusion

Adding and subtracting terms with variables is an essential skill in algebra. Remember that you can only combine like terms, which have the same variable and the same power. By practicing and solving different types of problems, you’ll become more confident in your algebra skills. Keep practicing and have fun with math!