Simplify 7a + 8b + 4a + 9b: Combining Like Terms Step by Step

Q: What exactly are 'like terms'?

Like terms have the exact same variable(s) raised to the same power. For example, $ 7a $ and $ 4a $ are like terms, but $ 7a $ and $ 8b $ are not.

Q: Why can't I multiply 11a and 17b to get 187ab?

Because addition and multiplication are different operations! When you see $ 11a + 17b $, the plus sign means keep them separate. Only multiply when you see terms directly next to each other like $ 11 \cdot 17 \cdot a \cdot b $.

Q: Do I need to write the terms in any special order?

Not required, but it's good practice to write variables in alphabetical order. So $ 11a + 17b $ is preferred over $ 17b + 11a $, though both are mathematically correct.

Q: What if I have three different variables like a, b, and c?

Same rules apply! Group each variable separately: $ 3a + 2b + 5c + 4a + 7b $ becomes $ 7a + 9b + 5c $. Just make sure each variable type stays together.

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

Your answer is fully simplified when you have no more like terms to combine. In $ 11a + 17b $, the terms $ a $ and $ b $ are different variables, so you're done!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:04 We'll use the commutative law and group like terms together

00:13 Combine terms

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$7a+8b+4a+9b=\text{?}$

2

Step-by-step solution

To simplify the expression $7a + 8b + 4a + 9b$ , we will follow these steps:

Step 1: Identify like terms. The expression contains terms involving $a$ ( $7a$ and $4a$ ) and terms involving $b$ ( $8b$ and $9b$ ).
Step 2: Combine the coefficients of like terms.
Step 3: Rewrite the simplified expression.

Step 1: The like terms involving $a$ are $7a$ and $4a$ .

Step 2: Add these coefficients: $7 + 4 = 11$ . Therefore, the combined term for $a$ is $11a$ .

Step 3: The like terms involving $b$ are $8b$ and $9b$ .

Step 4: Add these coefficients: $8 + 9 = 17$ . Therefore, the combined term for $b$ is $17b$ .

Thus, the expression simplifies to $11a + 17b$ .

The correct answer choice is: $11a + 17b$ .

3

Final Answer

$11a+17b$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Combine only terms with identical variables and powers
Technique: Add coefficients: 7a + 4a = (7+4)a = 11a
Check: Count terms before and after: 4 terms become 2 terms ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients of different variables
Don't add 7a + 8b to get 15ab = wrong variable combination! This creates a completely different term type. Always combine only terms with identical variables: 7a + 4a = 11a and 8b + 9b = 17b separately.

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

What exactly are 'like terms'?

+

Like terms have the exact same variable(s) raised to the same power. For example, $7a$ and $4a$ are like terms, but $7a$ and $8b$ are not.

Why can't I multiply 11a and 17b to get 187ab?

+

Because addition and multiplication are different operations! When you see $11a + 17b$ , the plus sign means keep them separate. Only multiply when you see terms directly next to each other like $11 \cdot 17 \cdot a \cdot b$ .

Do I need to write the terms in any special order?

+

Not required, but it's good practice to write variables in alphabetical order. So $11a + 17b$ is preferred over $17b + 11a$ , though both are mathematically correct.

What if I have three different variables like a, b, and c?

+

Same rules apply! Group each variable separately: $3a + 2b + 5c + 4a + 7b$ becomes $7a + 9b + 5c$ . Just make sure each variable type stays together.

How do I know if my final answer is fully simplified?

+

Your answer is fully simplified when you have no more like terms to combine. In $11a + 17b$ , the terms $a$ and $b$ are different variables, so you're done!

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