Simplify 13x+4y-(6x-3y): Combining Like Terms in Algebraic Expressions

Distributive Property with Negative Signs

13x+4y(6x3y)=? 13x+4y-(6x-3y)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this together!
00:10 Remember, when multiplying a negative number by a positive number, the result is always negative.
00:18 And, when multiplying two negative numbers, the result is always positive.
00:25 Now, let's group the factors carefully step by step.
00:36 Great job! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

13x+4y(6x3y)=? 13x+4y-(6x-3y)=\text{?}

2

Step-by-step solution

To begin with we address the parenthesis:

Remember that:

When we multiply a positive number by a negative number, the result will be negative.

When we multiply a negative number by a negative number, the result will be positive.

Thus we obtain the following:

13x+4y6x+3y= 13x+4y-6x+3y=

We then join the x coefficients:

13x6x=7x 13x-6x=7x

We join the y coefficients:

4y+3y=7y 4y+3y=7y

Lastly we obtain:

7x+7y 7x+7y

3

Final Answer

7x+7y 7x+7y

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: The negative sign affects each term inside parentheses
  • Technique: Change -(6x-3y) to -6x+3y before combining
  • Check: Combine like terms: 13x-6x=7x and 4y+3y=7y ✓

Common Mistakes

Avoid these frequent errors
  • Not distributing the negative sign to all terms
    Don't write -(6x-3y) as -6x-3y = wrong signs! The negative distributes to both terms, making -3y become +3y. Always distribute the negative sign to every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

\( 70:(14\times5)= \)

FAQ

Everything you need to know about this question

Why does the -3y become +3y after removing parentheses?

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When you have a negative sign in front of parentheses, it multiplies each term inside. So (3y)=+3y -(−3y) = +3y because negative times negative equals positive!

How do I know which terms are like terms?

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Like terms have the exact same variable part. In this problem, 13x and 6x are like terms (both have x), and 4y and 3y are like terms (both have y).

Can I combine 7x and 7y to get 14xy?

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No! You cannot combine terms with different variables. 7x+7y 7x + 7y stays as 7x+7y 7x + 7y - they are not like terms and cannot be combined.

What if I forget to distribute the negative sign?

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You'll get the wrong answer! Always write out each step: first distribute the negative, then identify like terms, then combine. Taking shortcuts often leads to sign errors.

Is there a way to check my work?

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Yes! Pick simple values for x and y (like x=1, y=1) and substitute into both the original expression and your answer. If they give the same result, you're correct!

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