Solve the Algebraic Expression: 12z + 3m - (m-z)

Algebraic Simplification with Parentheses Distribution

12z+3m(mz)=? 12z+3m-(m-z)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:07 Note, when multiplying negative by positive the result is always negative
00:12 Note, when multiplying negative by negative the result is always positive
00:20 Let's gather terms
00:25 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

12z+3m(mz)=? 12z+3m-(m-z)=\text{?}

2

Step-by-step solution

We begin by addressing 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.

Hence we obtain the following calculation:

12z+3mm+z= 12z+3m-m+z=

Next we join together the z coefficients:

12z+z=13z 12z+z=13z

We then join together the m coefficients:

3mm=2m 3m-m=2m

Finally we obtain the following:

13z+2m 13z+2m

3

Final Answer

13z+2m 13z+2m

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: When subtracting parentheses, change signs of all terms inside
  • Technique: Transform -(m-z) into -m+z by distributing the negative
  • Check: Combine like terms: 12z+z=13z and 3m-m=2m ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute the negative sign through parentheses
    Don't just remove parentheses from -(m-z) = 12z+3m-m-z = 11z+2m! This ignores the negative sign outside parentheses. Always distribute the negative: -(m-z) = -m+z, giving 12z+3m-m+z = 13z+2m.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does -(m-z) become -m+z and not -m-z?

+

The negative sign in front of parentheses acts like multiplying by -1. So (mz)=(1)(m)+(1)(z)=m+z -(m-z) = (-1)(m) + (-1)(-z) = -m + z . The double negative becomes positive!

How do I remember which terms to combine?

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Look for terms with the same variable! In this problem: z terms (12z and +z) combine to 13z, and m terms (3m and -m) combine to 2m.

What if there were numbers without variables?

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Treat them as constant terms and combine them separately from the variable terms. For example, if you had +5 and -3, they would combine to +2.

Can I work from left to right instead?

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You can, but it's safer to handle parentheses first using the distributive property, then combine like terms. This prevents sign errors and follows the proper order of operations.

How can I check if my final answer is correct?

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Substitute specific values for the variables into both the original expression and your simplified answer. If they give the same result, your simplification is correct! ✓

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