Math Problem Statement

Simplify the following expression: (1 point) 2x − 6y + 3x2 + 7y − 14x.

3x2 + 12x + y

3x2 − 12x − y

3x2 − 12x + y

3x2 − 12x − 13y

Solution

Let's simplify the expression step by step:

Given expression: 2x6y+3x2+7y14x2x - 6y + 3x^2 + 7y - 14x

  1. Combine like terms:
    • For the xx-terms: 2x14x=12x2x - 14x = -12x
    • For the yy-terms: 6y+7y=y-6y + 7y = y
    • The 3x23x^2 term stays as it is.

So, the simplified expression becomes: 3x212x+y3x^2 - 12x + y

Thus, the correct answer is: 3x² − 12x + y

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:

  1. How do you identify like terms in an algebraic expression?
  2. What would the result be if we had 2x2-2x^2 instead of 3x23x^2?
  3. How would the expression change if there were no yy-terms?
  4. Can you simplify 5x+3x2x+7x22x5x + 3x^2 - x + 7x^2 - 2x?
  5. What is the role of coefficients in simplifying expressions?

Tip: Always group like terms when simplifying expressions, which include terms with the same variable and exponent.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions
Combining Like Terms

Formulas

Expression Simplification by Combining Like Terms

Theorems

No specific theorems used, just basic algebraic operations

Suitable Grade Level

Grades 7-9