Math Problem Statement

Given the equation 10 + 3Y + BX - Y = ..., identify variables, coefficients, constants, factors, and terms. Also, determine which algebraic expressions among the choices contain like terms.

Solution

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  1. Equation given: 10+3Y+BXY=10 + 3Y + BX - Y = \ldots

    The problem under this asks to identify:

    • Variables
    • Coefficients
    • Constants
    • Factors
    • Terms
  2. The second problem asks:

    • Which of the following algebraic expressions contains terms that are of the same type (or "like terms")?
    • The given choices are:
      • a.p4p2a. p - 4p^2
      • b.3x2+2x2b. 3x^2 + 2x^2
      • c.2xyxyc. 2xy - xy
      • d.8p9d. 8p - 9
      • e.12p29qe. 12p^2 - 9q
      • f.7p8pf. 7p - 8p

For the first question, we would analyze the equation:

  • Variables: YY, XX, and BB
  • Coefficients: 3 for 3Y3Y, and BB for BXBX (since the coefficient of XX is BB)
  • Constant: 10
  • Factors: The parts of each term involving variables and their coefficients
  • Terms: 10, 3Y3Y, BXBX, Y-Y

For the second question, we look for expressions where the terms are like terms:

  • Like terms have the same variables raised to the same power.
  • b.3x2+2x2b. 3x^2 + 2x^2 and f.7p8pf. 7p - 8p are like terms because their variables and exponents are identical.

Would you like a detailed explanation of any of these points, or help with solving the full problems?

Here are 5 follow-up questions based on this:

  1. Can you explain the difference between a coefficient and a constant?
  2. Why are like terms important in simplifying algebraic expressions?
  3. What operation is usually performed on like terms in algebra?
  4. How do you identify factors in an algebraic expression?
  5. How can we simplify the expression 3x2+2x23x^2 + 2x^2?

Tip: When dealing with algebra, always try to group like terms first to simplify the equation easily.

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Math Problem Analysis

Mathematical Concepts

Algebra
Like Terms
Expressions
Variables
Coefficients

Formulas

None explicitly, but simplifying algebraic expressions

Theorems

None explicitly, but general algebraic rules on like terms and expressions

Suitable Grade Level

Grades 7-9