Math Problem Statement

Simplify each expression from the worksheet.

Solution

I see the worksheet you uploaded focuses on simplifying algebraic expressions. Let's work through the simplification of a few problems to illustrate the process, and then I can assist with any specific questions you might have.

Here are the steps for the first few:

  1. Problem 11: 4p+8p+104p + 8p + 10

    • Combine like terms: 4p+8p=12p4p + 8p = 12p.
    • Answer: 12p+1012p + 10.
  2. Problem 12: 12+2x14x+812 + 2x - 14x + 8

    • Combine like terms for xx: 2x14x=12x2x - 14x = -12x.
    • Combine constants: 12+8=2012 + 8 = 20.
    • Answer: 12x+20-12x + 20.
  3. Problem 13: a74a+2a - 7 - 4a + 2

    • Combine like terms for aa: a4a=3aa - 4a = -3a.
    • Combine constants: 7+2=5-7 + 2 = -5.
    • Answer: 3a5-3a - 5.
  4. Problem 14: r2s+2r8sr - 2s + 2r - 8s

    • Combine like terms for rr: r+2r=3rr + 2r = 3r.
    • Combine like terms for ss: 2s8s=10s-2s - 8s = -10s.
    • Answer: 3r10s3r - 10s.
  5. Problem 15: x+4x+48xx + 4x + 4 - 8x

    • Combine like terms for xx: x+4x8x=3xx + 4x - 8x = -3x.
    • Constant term remains +4+4.
    • Answer: 3x+4-3x + 4.

Would you like detailed solutions for all problems, or do you have specific questions about any particular ones?

Follow-Up Questions

  1. How do you identify and combine like terms in algebraic expressions?
  2. What is the process for handling both positive and negative coefficients when combining terms?
  3. Can I help you with any additional explanations on simplifying expressions involving multiple variables?
  4. Do you have specific questions about simplifying expressions with distributive properties?
  5. Would you like assistance with more complex expressions, such as those involving parentheses?

Tip: Always start by grouping terms with the same variable or constants to simplify expressions step by step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Combining Like Terms

Formulas

Combining like terms by adding or subtracting coefficients

Theorems

Properties of addition and subtraction in algebra

Suitable Grade Level

Grades 6-8