Simplify 8y+4x-(13x+8y): Multi-Variable Expression Challenge

Distributive Property with Negative Signs

8y+4x(13x+8y)=? 8y+4x-(13x+8y)=\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 that when multiplying negative by positive, the result is always negative:
00:19 Let's gather terms
00:27 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

8y+4x(13x+8y)=? 8y+4x-(13x+8y)=\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 negative will give us negative numbers:

8y+4x13x8y= 8y+4x-13x-8y=

Now we group the X factors:

4x13x=9x 4x-13x=-9x

Now we group the Y factors:

8y8y=0 8y-8y=0

Now we obtain:

9x -9x

3

Final Answer

9x -9x

Key Points to Remember

Essential concepts to master this topic
  • Distribution: Negative sign affects all terms inside parentheses
  • Technique: Change (13x+8y) -(13x+8y) to 13x8y -13x-8y
  • Check: Combine like terms: 8y8y=0 8y-8y=0 and 4x13x=9x 4x-13x=-9x

Common Mistakes

Avoid these frequent errors
  • Not distributing negative sign to all terms
    Don't change -(13x+8y) to -13x+8y = wrong answer! The negative affects BOTH terms inside parentheses. Always distribute the negative to every single term: -(13x+8y) becomes -13x-8y.

Practice Quiz

Test your knowledge with interactive questions

\( 60:(10\times2)= \)

FAQ

Everything you need to know about this question

Why does the negative sign change both terms?

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The negative sign acts like multiplying by -1. When you multiply 1×(13x+8y) -1 \times (13x+8y) , you get 13x8y -13x-8y because every term gets multiplied.

What if I forget to distribute the negative?

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You'll get the wrong answer! For example, if you write 8y+4x13x+8y 8y+4x-13x+8y instead of 8y+4x13x8y 8y+4x-13x-8y , you'd get 16y-9x instead of the correct -9x.

How do I combine like terms after distributing?

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Group terms with the same variable: put all x terms together and all y terms together. Then add or subtract the coefficients (numbers in front).

What happens when like terms cancel out completely?

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When coefficients are opposites like +8y +8y and 8y -8y , they equal zero and disappear from your answer. This is totally normal!

Can I check my work somehow?

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Yes! Substitute any value for the variables into both the original expression and your simplified answer. If they give the same result, you're correct!

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