Find the Missing Coefficient: Solving ?(2x+y)=6x+3y

Q: How do I know what number to factor out?

Look for the greatest common factor (GCF) of all terms. In $ 6x + 3y $, both 6 and 3 are divisible by 3, so factor out 3.

Q: Can the missing factor be a fraction or negative number?

Yes! The distributive property works with any real number, including fractions, decimals, and negative numbers. Always check your arithmetic carefully.

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

Try expanding what you think the answer might be. For example, test if 3 works by calculating $ 3(2x + y) = 6x + 3y $.

Distributive Property with Missing Factors

Fill in the missing value:

$?(2x+y)=6x+3y$

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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 factors 2 and 3

00:14 Let's mark the common factors

00:24 Let's take out the common factors from the parentheses

00:28 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 value:

$?(2x+y)=6x+3y$

Step-by-step solution

To solve this problem, we need to equate the expression $?(2x+y)$ to $6x+3y$ and solve for the missing factor.

Step 1: Analyze the expression $6x + 3y$ .

Notice that both terms, $6x$ and $3y$ , have a common factor of 3.

Thus, we can factor the expression as $3(2x + y)$ .

Step 2: Equate the factored form $3(2x + y)$ with the original form $?(2x + y)$ .

If $?(2x + y) = 3(2x + y)$ , then the missing factor $?$ must be 3.

Therefore, the missing number that satisfies the equation $?(2x+y)=6x+3y$ is $3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Factoring: Look for common factors in all terms first
Technique: Factor out 3 from $6x + 3y$ to get $3(2x + y)$
Check: Multiply $3(2x + y) = 6x + 3y$ matches original ✓

Common Mistakes

Avoid these frequent errors

Trying to match coefficients separately
Don't match 6x with 2x and 3y with y separately = wrong thinking! This ignores the distributive property structure. Always factor out the common factor from all terms first to see the pattern.

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 know what number to factor out?

Look for the greatest common factor (GCF) of all terms. In $6x + 3y$ , both 6 and 3 are divisible by 3, so factor out 3.

What if the coefficients don't have an obvious common factor?

Check if the expression can be written as something times the given binomial. Work backwards: if $?(2x + y)$ equals your expression, what would ? need to be?

Can the missing factor be a fraction or negative number?

Yes! The distributive property works with any real number, including fractions, decimals, and negative numbers. Always check your arithmetic carefully.

How can I verify my answer is correct?

Multiply your factor by the binomial using the distributive property. If you get the original expression $6x + 3y$ , your answer is right!

What if I can't see the pattern right away?

Try expanding what you think the answer might be. For example, test if 3 works by calculating $3(2x + y) = 6x + 3y$ .

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