Simplify the Expression: 25x+33y+6z-(14-(-12y)-3z)

Algebraic Expression Simplification with Nested Parentheses

25x+33y+6z(14(12y)3z)=? 25x+33y+6z-(14-(-12y)-3z)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Always solve parentheses first
00:07 Always solve the "innermost" parentheses first
00:12 Note, negative times negative is always positive
00:26 Note, negative times positive is always negative
00:36 Note, negative times negative is always positive
00:47 Group terms
01:03 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

25x+33y+6z(14(12y)3z)=? 25x+33y+6z-(14-(-12y)-3z)=\text{?}

2

Step-by-step solution

First, let's address the expression in the innermost parentheses.

Remember that when we multiply a negative number by a negative number, the result will be positive.

Now we get:

25x+33y+6z(14+12y3z)= 25x+33y+6z-(14+12y-3z)=

Let's now look at the expression in parentheses while remembering rule:

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

We get:

25x+33y+6z1412y+3z= 25x+33y+6z-14-12y+3z=

Now let's combine the y coefficients:

33y12y=21y 33y-12y=21y

Now let's combine the z coefficients:

6z+3z=9z 6z+3z=9z

This leaves us with:

25x+21y+9z14 25x+21y+9z-14

3

Final Answer

25x+21y+9z14 25x+21y+9z-14

Key Points to Remember

Essential concepts to master this topic
  • Rule: Work from innermost parentheses outward when simplifying expressions
  • Technique: Change (14(12y)3z) -(14-(-12y)-3z) to 14+12y+3z -14+12y+3z
  • Check: Combine like terms: 33y12y=21y 33y-12y=21y and 6z+3z=9z 6z+3z=9z

Common Mistakes

Avoid these frequent errors
  • Incorrectly distributing the negative sign
    Don't just change the signs of some terms when distributing a negative = wrong coefficients! Students often miss that -(14-(-12y)) becomes -14+12y, not -14-12y. Always distribute the negative sign to every term inside the parentheses and remember that two negatives make a positive.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does -(-12y) become +12y?

+

When you have a negative times a negative, the result is always positive! Think of it as: 1×(12y)=+12y -1 \times (-12y) = +12y . This is a fundamental rule in algebra.

How do I handle the minus sign in front of the parentheses?

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The minus sign acts like multiplying by -1. Distribute it to every single term inside the parentheses: (14(12y)3z)=14+12y+3z -(14-(-12y)-3z) = -14+12y+3z .

What order should I simplify this expression?

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Always work from the inside out:

  • First: Handle (12y)=+12y -(-12y) = +12y
  • Second: Distribute the negative sign
  • Finally: Combine like terms

How do I combine like terms correctly?

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Group terms with the same variable: all x terms together, all y terms together, all z terms together, and constants together. Then add or subtract their coefficients.

What if I get confused with all the negative signs?

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Take it step by step! Write out each step clearly and double-check your work. Remember: when distributing a negative, every term inside changes sign.

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