Simplify the Expression: 35y-(10y+35z+12y) Step by Step

Distributive Property with Negative Signs

35y(10y+35z+12y)=? 35y-(10y+35z+12y)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Note, when multiplying negative by positive it's always negative:
00:25 Let's gather terms
00:33 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

35y(10y+35z+12y)=? 35y-(10y+35z+12y)=\text{?}

2

Step-by-step solution

First, we open the parentheses and change the sign accordingly.

Since there are only positive numbers inside the parentheses, multiplying by minus will give us negative numbers:

35y10y35z12y= 35y-10y-35z-12y=

Now we group the factors and:

35y10y12y=25y12y=13y 35y-10y-12y=25y-12y=13y

Now we obtain:

13y35z 13y-35z

3

Final Answer

13y35z 13y-35z

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Distribute negative sign to each term inside parentheses
  • Technique: Change (10y+35z+12y) -(10y+35z+12y) to 10y35z12y -10y-35z-12y
  • Check: Combine like terms: 35y10y12y=13y 35y-10y-12y = 13y

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute the negative sign to all terms
    Don't write 35y - 10y + 35z + 12y = 57y + 35z! This ignores the negative sign before the parentheses and gives a completely wrong answer. Always distribute the negative sign to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to change all the signs inside the parentheses?

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The negative sign in front of the parentheses acts like multiplying by -1. This means every term inside gets its sign flipped: positive becomes negative, and negative becomes positive.

What's the difference between 35y - (10y + 35z + 12y) and 35y - 10y + 35z + 12y?

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The first expression has a negative sign before parentheses, so you must distribute it. The second has no parentheses, so you work left to right. They give completely different answers!

How do I combine like terms after distributing?

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Group terms with the same variable: all y-terms together, all z-terms together. Then add or subtract the coefficients: 35y10y12y=13y 35y - 10y - 12y = 13y .

Can I work inside the parentheses first before distributing?

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Sometimes yes, but be careful! In this problem, 10y+12y=22y 10y + 12y = 22y , giving us 35y(22y+35z) 35y - (22y + 35z) . Then distribute the negative sign.

What if there are no like terms to combine?

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That's okay! Your final answer might have multiple variables like 13y35z 13y - 35z . Just make sure all terms are simplified and in standard form.

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