Solve (m+n)(4+?) = n²+mn+4m+4n: Find the Missing Term

Q: How do I know which term is missing in the parentheses?

Use the distributive property to expand what you have, then compare it to the target expression. The missing piece will become clear when you match terms!

Q: What if I expand and get terms in a different order?

That's totally fine! Addition is commutative, so $4m + mn + 4n + n^2$ equals $n^2 + mn + 4m + 4n$. Just make sure all terms match.

Q: Can I work backwards from the expanded form?

Yes! Look at the target expression and think: what would I multiply to get these terms? For example, to get $n^2$, you need $n \times n$.

Q: Why does the distributive property work here?

The distributive property says $a(b+c) = ab + ac$. When you have $(m+n)(4+?)$, you're distributing both m and n to both terms in the second parentheses.

Q: What if there were multiple missing terms?

Use the same method! Expand what you can, then compare term by term with the target. Each missing piece will have a specific pattern you can identify.

Algebraic Expansion with Missing Terms

Complete the missing element

$(m+n)(4+?)=n^2+mn+4m+4n$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing term

00:03 Open parentheses properly, multiply each factor by each factor

00:34 Group terms and reduce what's possible

00:50 Compare the corresponding terms

00:55 This is the value ?, now let's check if it fits

01:02 Compare the corresponding terms, find the value ? we found

01:10 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

Complete the missing element

$(m+n)(4+?)=n^2+mn+4m+4n$

Step-by-step solution

To solve this problem, we'll apply the distributive property to expand and match the expressions:

Step 1: Expand $(m+n)(4+?)$ using distributive property: $(m+n)(4+n) = m(4+n) + n(4+n)$ .
Step 2: This gives us $4m + mn + 4n + n^2$ .
Step 3: Compare this to the expression $n^2 + mn + 4m + 4n$ .

The expanded expression matches the target expression, so the missing term in $(m+n)(4+?)$ is indeed $n$ .

Therefore, the complete expression is $(m+n)(4+n)$ .

Final Answer

$n$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term by every term in parentheses
Technique: Expand $(m+n)(4+?)$ to get $4m + m? + 4n + n?$
Check: Match expanded form to given expression term by term ✓

Common Mistakes

Avoid these frequent errors

Guessing the missing term without expanding
Don't just guess n without showing work = wrong reasoning! This skips the crucial expansion step and doesn't verify the answer. Always expand (m+n)(4+?) completely and compare each term to the target expression.

Practice Quiz

Test your knowledge with interactive questions

It is possible to use the distributive property to simplify the expression below?

What is its simplified form?

$$ (ab)(c d) $$

$$

FAQ

Everything you need to know about this question

How do I know which term is missing in the parentheses?

Use the distributive property to expand what you have, then compare it to the target expression. The missing piece will become clear when you match terms!

What if I expand and get terms in a different order?

That's totally fine! Addition is commutative, so $4m + mn + 4n + n^2$ equals $n^2 + mn + 4m + 4n$ . Just make sure all terms match.

Can I work backwards from the expanded form?

Yes! Look at the target expression and think: what would I multiply to get these terms? For example, to get $n^2$ , you need $n \times n$ .

Why does the distributive property work here?

The distributive property says $a(b+c) = ab + ac$ . When you have $(m+n)(4+?)$ , you're distributing both m and n to both terms in the second parentheses.

What if there were multiple missing terms?

Use the same method! Expand what you can, then compare term by term with the target. Each missing piece will have a specific pattern you can identify.

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