Solve: Combining Like Terms in 5a + 3a + 8b + 10b

Q: Why can't I combine 8a and 18b into one term?

Different variables cannot be combined! Think of a and b as different objects - you can't add apples and bananas to get "applenanas." Keep them separate: 8a + 18b.

Q: What exactly are 'like terms'?

Like terms have exactly the same variable part. For example: 5a and 3a are like terms (both have 'a'), but 5a and 8b are unlike terms (different variables).

Q: Do I add or multiply the numbers in front?

You add the coefficients (numbers in front)! For 5a + 3a, add: 5 + 3 = 8, so the result is 8a. Never multiply coefficients when combining like terms.

Q: How do I know my final answer is fully simplified?

Check that you've combined all possible like terms. In your final answer, no two terms should have the same variable part. If they do, you can still combine them!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's simplify the expression.

00:09 First, identify the correct variables.

00:14 Next, use the commutative law to rearrange the variables.

00:22 Now, gather similar terms together.

00:31 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$5a+3a+8b+10b=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the like terms in the expression.
Step 2: Combine these like terms by adding their coefficients.

Now, let's work through each step:

Step 1: In the expression $5a + 3a + 8b + 10b$ , we have two types of like terms:

Terms involving $a$ : $5a$ and $3a$ .
Terms involving $b$ : $8b$ and $10b$ .

Step 2: Combine like terms:

For the terms involving $a$ : Combine $5a + 3a$ to get $8a$ .
For the terms involving $b$ : Combine $8b + 10b$ to get $18b$ .

The simplified expression combining all the terms is $8a + 18b$ .

Therefore, the solution to the problem is $8a + 18b$ .

3

Final Answer

$8a+18b$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Terms with identical variable parts can be combined together
Technique: Add coefficients: 5a + 3a = (5+3)a = 8a
Check: Count variable types separately: a-terms and b-terms stay distinct ✓

Common Mistakes

Avoid these frequent errors

Combining unlike terms or multiplying coefficients with variables
Don't add 5a + 8b to get 13ab or multiply to get 40ab! Variables with different letters cannot be combined. Always keep a-terms separate from b-terms and only add coefficients of identical variable parts.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

Why can't I combine 8a and 18b into one term?

+

Different variables cannot be combined! Think of a and b as different objects - you can't add apples and bananas to get "applenanas." Keep them separate: 8a + 18b.

What exactly are 'like terms'?

+

Like terms have exactly the same variable part. For example: 5a and 3a are like terms (both have 'a'), but 5a and 8b are unlike terms (different variables).

Do I add or multiply the numbers in front?

+

You add the coefficients (numbers in front)! For 5a + 3a, add: 5 + 3 = 8, so the result is 8a. Never multiply coefficients when combining like terms.

What if I have more than two like terms?

+

Just keep adding all the coefficients! For example: 2x + 5x + 3x = (2+5+3)x = 10x. Group all like terms together first, then add their coefficients.

How do I know my final answer is fully simplified?

+

Check that you've combined all possible like terms. In your final answer, no two terms should have the same variable part. If they do, you can still combine them!

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