In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

Verified step by step guidance

1. Step 1: Begin by simplifying the expression inside the brackets. Combine like terms within [(4y) + (−4y)]. Since 4y and −4y are additive inverses, their sum is 0. This simplifies the brackets to [0].
2. Step 2: Rewrite the expression with the simplified brackets. The expression now becomes 1/3(3x) + 0.
3. Step 3: Simplify the term 1/3(3x). Multiply 1/3 by 3x, which results in x.
4. Step 4: Combine the simplified terms. Since the second term is 0, the expression simplifies to just x.
5. Step 5: The final expression without parentheses is x.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to eliminate parentheses by distributing a factor across terms inside the parentheses. In the given expression, 1/3(3x) can be simplified by multiplying 1/3 by 3x, resulting in x.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. In the expression [(4y) + (−4y)], the terms 4y and -4y are like terms, and their sum is zero, which simplifies the expression further.

Simplifying Expressions

Simplifying expressions means rewriting them in a more concise form by performing operations and combining like terms. This process often involves applying the Distributive Property and combining like terms to eliminate parentheses and reduce the expression to its simplest form.