Simplify the Expression: 10y-(5y+3z) Step-by-Step

Distributive Property with Negative Signs

10y(5y+3z)=? 10y-(5y+3z)=\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 the result is always negative:
00:14 Let's collect terms
00:20 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

10y(5y+3z)=? 10y-(5y+3z)=\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 the minus will give us negative numbers:

10y5y3z= 10y-5y-3z=

Now we group the Y factors:

10y5y=5y 10y-5y=5y

Now we obtain:

5y3z 5y-3z

3

Final Answer

5y3z 5y-3z

Key Points to Remember

Essential concepts to master this topic
  • Distributive Rule: Apply negative sign to each term inside parentheses
  • Technique: Transform 10y-(5y+3z) into 10y-5y-3z by distributing
  • Check: Substitute values: if y=2, z=1, then 5(2)-3(1)=7 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply negative sign to all terms
    Don't just remove parentheses without changing signs = 10y-5y+3z = wrong answer! The negative outside affects every term inside the parentheses. Always distribute the negative sign to each term: 10y-5y-3z.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does the plus sign inside become a minus?

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The negative sign outside the parentheses acts like multiplying by -1. So (+3z)=3z -(+3z) = -3z . Think of it as: the opposite of positive is negative.

What if there were already negative terms inside?

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The rule stays the same! A negative outside flips all signs inside. So (5y3z) -(5y-3z) becomes 5y+3z -5y+3z . Two negatives make a positive!

How do I combine like terms after distributing?

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Look for terms with the same variable and exponent. Here, 10y5y 10y-5y combines to 5y 5y , but y y and z z terms cannot be combined.

Can I work from right to left instead?

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You must follow the order of operations! Always handle parentheses first by distributing, then combine like terms. Working left to right helps avoid sign errors.

What if I get confused with the signs?

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Write each step clearly! First: 10y(5y+3z) 10y-(5y+3z) . Then: 10y5y3z 10y-5y-3z . Finally: 5y3z 5y-3z . Taking your time prevents mistakes.

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