Simplify the Expression: 31x+5z-(34x-(-13z))

Distributive Property with Nested Parentheses

31x+5z(34x(13z))=? 31x+5z-(34x-(-13z))=\text{?}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this math problem together.
00:15 Remember, when you multiply a negative by another negative, the result is positive.
00:27 But, when you multiply a negative by a positive, the result is negative.
00:40 Next, we'll group the factors to simplify.
00:54 And that gives us the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

31x+5z(34x(13z))=? 31x+5z-(34x-(-13z))=\text{?}

2

Step-by-step solution

We begin by addressing the innermost parentheses:

Remember that:

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

Thus we obtain:

31x+5z(34x+13z)= 31x+5z-(34x+13z)=

Next we address the exercise within the parentheses:

Remember that:

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

31x+5z34x13z= 31x+5z-34x-13z=

We join the x coefficients:

31x34x=3x 31x-34x=-3x

We join the z coefficients:

5z13x=8z 5z-13x=-8z

We obtain the following:

3x8z -3x-8z

3

Final Answer

3x8z -3x-8z

Key Points to Remember

Essential concepts to master this topic
  • Order: Always work from innermost parentheses outward first
  • Signs: Negative times negative equals positive: (13z)=+13z-(- 13z) = +13z
  • Check: Combine like terms separately: x-terms give -3x, z-terms give -8z ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the double negative in nested parentheses
    Don't treat -(-13z) as just -13z = wrong sign on z-terms! The double negative becomes positive, so -(-13z) = +13z. Always carefully track each negative sign through nested parentheses.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why does -(-13z) become +13z?

+

When you have a negative outside parentheses and a negative inside, they multiply to make positive! Think of it as (1)×(13z)=+13z(-1) \times (-13z) = +13z.

How do I keep track of all the negative signs?

+

Work step by step! First handle the innermost parentheses (13z)=+13z-(-13z) = +13z, then distribute the outer negative: (34x+13z)=34x13z-(34x + 13z) = -34x - 13z.

What if I get confused with the parentheses?

+

Rewrite each step clearly! Start with 31x+5z(34x(13z))31x + 5z - (34x - (-13z)), then 31x+5z(34x+13z)31x + 5z - (34x + 13z), then 31x+5z34x13z31x + 5z - 34x - 13z.

Can I combine x and z terms together?

+

No! You can only combine like terms. The x-terms (31x and -34x) combine separately from z-terms (5z and -13z). Variables with different letters stay separate.

How do I know which terms to combine?

+

Look for terms with the same variable and same power. Here: 31x34x=3x31x - 34x = -3x and 5z13z=8z5z - 13z = -8z. Different variables never combine!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations