Question

Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. For example, compare simplifying 3(x – 2) + (x – 1) with 3(5 – 2) + (5 – 1).

A. Algebraic expressions involve variables, while numeric expressions involve only numbers.
B. Expanding algebraic expressions includes distributing terms, whereas simplifying numeric expressions involves basic arithmetic operations.
C. Expanding algebraic expressions is only applicable to polynomials, while simplifying numeric expressions applies to all types of numbers.
D. Simplifying algebraic expressions is a more complex process compared to simplifying numeric expressions.

Answer 1

Expanding algebraic expressions involves distributivity and combining like terms, while simplifying numeric expressions involves basic arithmetic operations on numbers.

Step-by-step explanation:

Expanding and simplifying algebraic expressions with simplifying numeric expressions have some similarities and differences.

When expanding algebraic expressions, we use properties of distributivity to open up parentheses and combine like terms. For example, when simplifying 3(x - 2) + (x - 1), we can distribute the 3 to both terms inside the first parentheses. Then, we can combine like terms to simplify the expression.

On the other hand, simplifying numeric expressions involves performing basic arithmetic operations on numbers. In the given example of simplifying 3(5 - 2) + (5 - 1), we simply evaluate the expressions inside the parentheses and then perform addition to get the final result.