Simplify the Expression: 13a+14b+17c-4a-2b-4b Using Like Terms

Q: What makes terms 'like terms' that can be combined?

Like terms must have exactly the same variable with exactly the same power. For example: 13a and -4a are like terms, but 13a and 14b are not!

Q: Why can't I just add all the numbers together?

Because variables represent different quantities! Adding 13a + 14b would be like adding 13 apples + 14 bananas - you can't get a single fruit type as the result.

Q: How do I handle the negative signs correctly?

Treat the negative sign as part of the coefficient. So $ -4a $ has coefficient -4, and $ -2b $ has coefficient -2. Then add: 14 + (-2) + (-4) = 8

Q: What if I have no like terms for a variable?

That's fine! Like the $ 17c $ term in this problem - it stays exactly the same in your final answer because there are no other c-terms to combine with.

Q: How can I organize my work to avoid mistakes?

Group like terms together first: Write all a-terms together, all b-terms together, etc. This makes it easier to see what needs to be combined and prevents mixing different variables.

Algebraic Simplification with Multiple Variables

^{$13a+14b+17c-4a-2b-4b=\text{?}$}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:03 Mark the variables

00:07 Use the commutative law and group like terms together

00:18 Combine factors

00:42 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

^{$13a+14b+17c-4a-2b-4b=\text{?}$}

Step-by-step solution

To solve the problem, we should simplify the expression by combining like terms:

Step 1: Identify like terms.
- The terms involving $a$ are $13a$ and $-4a$ .
- The terms involving $b$ are $14b$ , $-2b$ , and $-4b$ .
- The term involving $c$ is $17c$ .
Step 2: Combine like terms by summing their coefficients:
- For $a$ -terms: $13a - 4a = (13 - 4)a = 9a$ .
- For $b$ -terms: $14b - 2b - 4b = (14 - 2 - 4)b = 8b$ .
The $c$ term remains unchanged as $17c$ .

Therefore, the simplified expression is $9a + 8b + 17c$ .

Checking the choices provided, we see that the correct answer is $9a + 8b + 17c$ , which matches choice .

Thus, the final simplified expression is $9a + 8b + 17c$ .

Final Answer

$9a+8b+17c$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Combine terms with identical variables and powers only
Technique: Group coefficients: 13a - 4a = (13 - 4)a = 9a
Check: Count original terms vs final terms: 6 terms → 3 terms ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients of different variables together
Don't combine 13a + 14b to get 27ab = completely wrong variable! Different variables (a, b, c) cannot be combined even if they have the same coefficient. Always keep different variables separate and only combine identical variable terms.

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 makes terms 'like terms' that can be combined?

Like terms must have exactly the same variable with exactly the same power. For example: 13a and -4a are like terms, but 13a and 14b are not!

Why can't I just add all the numbers together?

Because variables represent different quantities! Adding 13a + 14b would be like adding 13 apples + 14 bananas - you can't get a single fruit type as the result.

How do I handle the negative signs correctly?

Treat the negative sign as part of the coefficient. So $-4a$ has coefficient -4, and $-2b$ has coefficient -2. Then add: 14 + (-2) + (-4) = 8

What if I have no like terms for a variable?

That's fine! Like the $17c$ term in this problem - it stays exactly the same in your final answer because there are no other c-terms to combine with.

How can I organize my work to avoid mistakes?

Group like terms together first: Write all a-terms together, all b-terms together, etc. This makes it easier to see what needs to be combined and prevents mixing different variables.

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