Simplify the Expression: 12x-(13x+4y) Step by Step

Distributive Property with Negative Signs

12x(13x+4y)=? 12x-(13x+4y)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Note, when multiplying negative by positive, the result is always negative:
00:15 Let's gather terms
00:21 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

12x(13x+4y)=? 12x-(13x+4y)=\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:

12x13x4y= 12x-13x-4y=

Now we group the x factors:

12x13x=1x 12x-13x=-1x

Now we obtain:

1x4y -1x-4y

3

Final Answer

x4y -x-4y

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Multiply negative sign by each term inside parentheses
  • Technique: Transform -(13x+4y) into -13x-4y before combining
  • Check: Substitute values to verify 12x-13x-4y = -x-4y ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute the negative sign to all terms
    Don't write 12x-13x+4y instead of 12x-13x-4y = wrong positive term! The negative outside parentheses must multiply every term inside. Always distribute the negative to each term: -(13x+4y) = -13x-4y.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(30-21)= \)

FAQ

Everything you need to know about this question

Why does the +4y become -4y when I remove parentheses?

+

The negative sign outside the parentheses acts like multiplying by -1. So -(+4y) becomes -4y, just like how -1 × 4 = -4!

Can I just ignore the parentheses and subtract normally?

+

No! The parentheses group terms together. You must distribute the negative sign to every term inside before combining like terms.

How do I combine 12x and -13x?

+

Think of it like this: if you have 12 apples and take away 13 apples, you're 1 apple short. So 12x - 13x = -1x or simply -x.

What if there were more terms inside the parentheses?

+

The same rule applies! Distribute the negative to every single term. For example: -(2x + 3y - 5z) = -2x - 3y + 5z

Why is the final answer -x-4y and not -x+4y?

+

Because we distributed the negative sign to both terms: -(13x + 4y) = -13x and -4y. The +4y became -4y after distribution.

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