Simplify the Expression: 3m-14n-(7m-3n) Step by Step

Q: Why does the negative sign in front of parentheses change both terms inside?

Think of the negative sign as multiplying by -1. Just like $ -1 \times (7m-3n) = -1 \times 7m + (-1) \times (-3n) = -7m + 3n $. Every term gets multiplied!

Q: How do I remember which terms to combine?

Like terms have the same variable and exponent. In this problem, combine all m terms together (3m and -7m) and all n terms together (-14n and +3n).

Q: What if I accidentally multiply the variables together?

Variables with different letters like m and n cannot be combined by multiplication unless specifically asked. Keep them separate: -4m and -11n stay as -4m-11n, not -44mn.

Q: Can I solve this problem in a different order?

Yes! You could rearrange terms first: $ 3m-7m-14n+3n $, then combine like terms. The key is to always distribute the negative sign before rearranging.

Q: How do I check if my final answer is correct?

Substitute simple values like m=1, n=1 into both the original expression and your answer. If $ 3(1)-14(1)-(7(1)-3(1)) $ equals $ -4(1)-11(1) $, you're right!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Note, when multiplying a negative by a positive, the result is always negative

00:10 Note, when multiplying a negative by a negative, the result is always positive

00:18 Let's gather terms

00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$3m-14n-(7m-3n)=\text{?}$

2

Step-by-step solution

We begin by addressing the parenthesis first:

Remember that:

When we multiply a positive number by a negative number the result will be negative.

When we multiply a negative number by a negative number the result will be positive.

Thus we obtain the following equation:

$3m-14n-7m+3n=$

Next we join the m coefficients:

$3m-7m=-4m$

We then join the n coefficients: $-14n+3n=-11n$

Finally we obtain:

$-4m-11n$

3

Final Answer

$-4m-11n$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Negative sign changes signs of all terms inside parentheses
Technique: Transform -(7m-3n) into -7m+3n by distributing the negative
Check: Combine like terms: 3m-7m=-4m and -14n+3n=-11n ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign to all terms
Don't just remove parentheses without distributing the negative: -(7m-3n) ≠ -7m-3n! This keeps the wrong sign on the second term and gives -4m-17n instead of -4m-11n. Always distribute the negative sign to every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why does the negative sign in front of parentheses change both terms inside?

+

Think of the negative sign as multiplying by -1. Just like $-1 \times (7m-3n) = -1 \times 7m + (-1) \times (-3n) = -7m + 3n$ . Every term gets multiplied!

How do I remember which terms to combine?

+

Like terms have the same variable and exponent. In this problem, combine all m terms together (3m and -7m) and all n terms together (-14n and +3n).

What if I accidentally multiply the variables together?

+

Variables with different letters like m and n cannot be combined by multiplication unless specifically asked. Keep them separate: -4m and -11n stay as -4m-11n, not -44mn.

Can I solve this problem in a different order?

+

Yes! You could rearrange terms first: $3m-7m-14n+3n$ , then combine like terms. The key is to always distribute the negative sign before rearranging.

How do I check if my final answer is correct?

+

Substitute simple values like m=1, n=1 into both the original expression and your answer. If $3(1)-14(1)-(7(1)-3(1))$ equals $-4(1)-11(1)$ , you're right!

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Simplify the Expression: 3m-14n-(7m-3n) Step by Step

Distributing Negative Signs with Variable Terms

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does the negative sign in front of parentheses change both terms inside?

How do I remember which terms to combine?

What if I accidentally multiply the variables together?

Can I solve this problem in a different order?

How do I check if my final answer is correct?

🌟 Unlock Your Math Potential

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