Simplify 3x-(7x+3y): Distributing Negative Signs in Algebraic Expressions

Distributive Property with Negative Signs

3x(7x+3y)=? 3x-(7x+3y)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve the problem together.
00:09 Remember, when you multiply a negative by a positive, the answer is always negative.
00:20 Now, let's gather all the terms.
00:26 Great job! And that's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3x(7x+3y)=? 3x-(7x+3y)=\text{?}

2

Step-by-step solution

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

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

3x7x3y= 3x-7x-3y=

Now we group the X factors:

3x7x=4x 3x-7x=-4x

Now we obtain:

4x3y -4x-3y

3

Final Answer

4x3y -4x-3y

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Negative sign distributes to every term inside parentheses
  • Technique: Transform -(7x+3y) into -7x-3y by multiplying each term
  • Check: Substitute values: 3(2)-(7(2)+3(1)) = 6-17 = -11 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute negative sign to all terms
    Don't just change the first term: 3x-7x+3y = -4x+3y is wrong! The negative distributes to BOTH 7x AND 3y. Always multiply every single term inside parentheses by the negative sign.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does the 3y become negative when there's a minus sign outside?

+

The negative sign in front of parentheses acts like multiplying by -1. So -(7x+3y) means -1(7x+3y) = -7x + (-3y) = -7x - 3y.

How do I remember to distribute to ALL terms?

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Think of the negative sign as a distribution truck that must visit every term inside the parentheses. No term gets left behind!

What if there are more terms inside the parentheses?

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The rule stays the same! If you have -(2x+5y-3z), distribute the negative to get -2x-5y+3z. Every single term changes sign.

Can I combine 3x and 3y together?

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No! You can only combine like terms that have the same variable. 3x and 3y are different variables, so they stay separate as -4x-3y.

What's the difference between 3x-7x and 3x-3y?

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3x-7x = -4x because both terms have the same variable x. But 3x-3y cannot be simplified further because x and y are different variables.

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