Multiple Choice: Type Your Answer Choice In The Blank

Multiple Choice: Type your answer choice in the blank. _____1. Simplify.

Identify the core assignment prompt, which asks to simplify an expression or problem, and remove any extraneous instructions, formatting instructions, or repetitive content. The primary task is to perform simplification on a given expression or equation, although the specific expression is not provided here.

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Simplification in mathematics involves reducing an expression to its most basic or most concise form without changing its value. This process typically includes combining like terms, applying the distributive property, and reducing fractions when necessary. In algebra, simplification helps to make equations easier to solve and to understand the relationships between variables clearly.

To effectively simplify an algebraic expression, the following steps are generally followed:

  1. Identify like terms. Like terms are terms that contain the same variables raised to the same powers. For example, in the expression 3x + 4x - 2, 3x and 4x are like terms and can be combined.
  2. Combine like terms. Add or subtract the coefficients of like terms. For instance, 3x + 4x becomes 7x.
  3. Apply distributive property if necessary. For expressions such as a(b + c), distribute to obtain ab + ac.
  4. Reduce fractions and constants. Simplify fractional expressions or constants to their lowest terms.

In practical applications, simplification helps in solving equations more efficiently, graphing functions accurately, and understanding the behavior of functions or expressions. It also provides a clearer view of the structure of the expression, which is essential for algebraic manipulations and problem-solving.

For example, suppose you have the expression 2(3x + 4) - 5x + 6. Simplifying this involves distributing 2, combining like terms, and reducing the expression to a simpler form:

2(3x + 4) - 5x + 6 = 6x + 8 - 5x + 6 = (6x - 5x) + (8 + 6) = x + 14.

The simplified expression is therefore x + 14, which is easier to use in further calculations or to interpret graphically.

In summary, simplification is a fundamental skill in algebra that entails reducing expressions to their simplest form for ease of use and clarity. It involves combining like terms, applying algebraic properties, and reducing constants or fractions to their lowest terms.

References

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  • Edwards, C. H., & Penney, D. (2012). Elementary Differential Equations and Boundary Value Problems. Pearson.
  • McGraw-Hill Education. (2015). High School Mathematics. McGraw-Hill Education.
  • Anton, H., Bivens, I., & Davis, S. (2013). Calculus: Early Transcendentals. Wiley.
  • Stewart, J. (2016). Calculus: Concepts and Contexts. Cengage Learning.
  • Fitzpatrick, P. (2014). Mathematics for the Liberal Arts. W. H. Freeman.
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