Factor the Expression: Finding Common Terms in 9a+8a

Q: Why can't I just add 9 + 8 = 17 and write 17a?

You can get the right final answer that way, but this problem specifically asks you to show the factoring process. You need to demonstrate that you can identify 'a' as the common factor and write it as $ a(9 + 8) $ first.

Q: How do I know what the common factor is?

Look at each term carefully! In $ 9a + 8a $, both terms have the variable 'a'. That's your common factor. The numbers 9 and 8 are the coefficients that stay inside the parentheses.

Q: What if there were different variables like 9a + 8b?

Great question! If you have $ 9a + 8b $, there's no common variable factor to pull out. You can only factor when terms share the same variable or number.

Q: Do I need to simplify 9 + 8 to get 17?

The problem asks for the factored form, so $ a(9 + 8) $ is the correct answer. You could simplify to $ 17a $, but that's not factored anymore!

Q: What if the common factor was a number instead of a variable?

Same process! If you had $ 6x + 6y $, the common factor is 6, so you'd write $ 6(x + y) $. Always look for what's the same in every term.

Factoring Expressions with Common Variables

We factored the expression $9a+8a$ into its basic terms:

$9\cdot a+8\cdot a$

Take out the common factor from the factored expression.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

We factored the expression $9a+8a$ into its basic terms:

$9\cdot a+8\cdot a$

Take out the common factor from the factored expression.

Step-by-step solution

We start with the expression $9a+8a$ .

First, we notice that both terms share a common factor of $a$ .

So, we factor out $a$ from each term:

$9a=a\cdot9$ and $8a = a\cdot 8$ .

This allows us to rewrite the expression as $a(9+8)$ .

Thus, the factored form is $a\left(9+8\right)$ .

Final Answer

$a\left(9+8\right)$

Key Points to Remember

Essential concepts to master this topic

Common Factor Rule: Look for variables or numbers that appear in every term
Factor Out Method: Write $9a + 8a = a(9 + 8)$
Verification: Distribute back: $a(9 + 8) = a(17) = 17a$ ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients without factoring out the variable
Don't just write $9a + 8a = 17a$ without showing the factoring step! This skips the required process and doesn't demonstrate understanding of common factors. Always identify and factor out the common variable first, then add the remaining coefficients.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 2x^2 $$

FAQ

Everything you need to know about this question

Why can't I just add 9 + 8 = 17 and write 17a?

You can get the right final answer that way, but this problem specifically asks you to show the factoring process. You need to demonstrate that you can identify 'a' as the common factor and write it as $a(9 + 8)$ first.

How do I know what the common factor is?

Look at each term carefully! In $9a + 8a$ , both terms have the variable 'a'. That's your common factor. The numbers 9 and 8 are the coefficients that stay inside the parentheses.

What if there were different variables like 9a + 8b?

Great question! If you have $9a + 8b$ , there's no common variable factor to pull out. You can only factor when terms share the same variable or number.

Do I need to simplify 9 + 8 to get 17?

The problem asks for the factored form, so $a(9 + 8)$ is the correct answer. You could simplify to $17a$ , but that's not factored anymore!

What if the common factor was a number instead of a variable?

Same process! If you had $6x + 6y$ , the common factor is 6, so you'd write $6(x + y)$ . Always look for what's the same in every term.

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