Solve 3m(? + ?) = 6mn + 9m: Finding Missing Values in Algebraic Distribution

Q: How do I find what to factor out?

Look for the greatest common factor in all terms. Both $ 6mn $ and $ 9m $ contain $ 3m $, so that's what you factor out.

Q: What if I can't see the common factor right away?

Break each term into its factors: $ 6mn = 2 \cdot 3 \cdot m \cdot n $ and $ 9m = 3 \cdot 3 \cdot m $. The common parts are $ 3m $.

Q: Why can't the answer be (n, 3)?

If you try $ 3m(n + 3) $, you get $ 3mn + 9m $, not $ 6mn + 9m $. The coefficient of the first term doesn't match!

Q: How do I check my factoring is correct?

Always distribute back! Take your factored form and multiply it out. If you get the original expression, your factoring is correct.

Q: What does the question mark represent?

Each question mark represents a missing term that, when multiplied by $ 3m $, gives you the corresponding term on the right side of the equation.

Factoring with Distributed Terms

Fill in the missing values:

$3m(?+?)=6mn+9m$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing values

00:03 Let's factor 6 into 3×2

00:10 Let's factor 9 into 3 and 3

00:25 Let's mark the common factors

00:29 Let's take out the common factors from the parentheses

00:39 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

Fill in the missing values:

$3m(?+?)=6mn+9m$

Step-by-step solution

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

Step 1: Look at the right side of the equation, $6mn + 9m$ , and factor out the common term $3m$ .
Step 2: Upon factoring, rewrite the expression as $3m(2n + 3)$ .
Step 3: Compare this factored form to the left side $3m(?+?)$ .
Step 4: Identify the terms inside the parentheses: $2n$ for the first place and $3$ for the second.

Following these steps:
Step 1: Recognize that both terms $6mn$ and $9m$ on the right have a common factor of $3m$ .
Step 2: Factor out $3m$ to get $3m(2n + 3)$ .
Step 3: Note that $3m(?+?)$ needs to match $3m(2n + 3)$ .
Step 4: Thus, the expressions inside the parentheses are $? = 2n$ and $? = 3$ .

Therefore, the solution to the problem is $2n, 3$ .

Final Answer

$2n,3$

Key Points to Remember

Essential concepts to master this topic

Factoring: Find the greatest common factor from all terms first
Technique: Factor out $3m$ from $6mn + 9m$ to get $3m(2n + 3)$
Check: Distribute back to verify: $3m(2n + 3) = 6mn + 9m$ ✓

Common Mistakes

Avoid these frequent errors

Trying to work backwards from individual terms
Don't guess what goes in the blanks by looking at $6mn$ and $9m$ separately = wrong combinations like $n, 3$ ! This ignores the common factor structure. Always factor out the greatest common factor first, then identify what remains inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

How do I find what to factor out?

Look for the greatest common factor in all terms. Both $6mn$ and $9m$ contain $3m$ , so that's what you factor out.

What if I can't see the common factor right away?

Break each term into its factors: $6mn = 2 \cdot 3 \cdot m \cdot n$ and $9m = 3 \cdot 3 \cdot m$ . The common parts are $3m$ .

Why can't the answer be (n, 3)?

If you try $3m(n + 3)$ , you get $3mn + 9m$ , not $6mn + 9m$ . The coefficient of the first term doesn't match!

How do I check my factoring is correct?

Always distribute back! Take your factored form and multiply it out. If you get the original expression, your factoring is correct.

What does the question mark represent?

Each question mark represents a missing term that, when multiplied by $3m$ , gives you the corresponding term on the right side of the equation.

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