In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(7y+2)

Verified step by step guidance

1. Distribute the 5 across the terms inside the parentheses (3y−2). This means multiplying 5 by each term: 5 * 3y and 5 * -2.
2. Simplify the distribution: 5 * 3y becomes 15y, and 5 * -2 becomes -10. So the expression now looks like 15y - 10 - (7y + 2).
3. Distribute the negative sign across the terms inside the parentheses (7y+2). This means multiplying -1 by each term: -1 * 7y and -1 * 2.
4. Simplify the distribution: -1 * 7y becomes -7y, and -1 * 2 becomes -2. So the expression now looks like 15y - 10 - 7y - 2.
5. Combine like terms: Add the terms with 'y' (15y and -7y) and combine the constants (-10 and -2). This will give you the simplified expression.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a set of parentheses. In the given expression, applying the distributive property to 5(3y - 2) means multiplying 5 by both 3y and -2, which simplifies the expression.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In the expression, after distributing, you will have terms involving 'y' and constant terms. Grouping these similar terms together allows for simplification, leading to a more concise expression.

Negative Sign Distribution

When a negative sign is in front of parentheses, it affects all terms inside the parentheses. For example, -(7y + 2) becomes -7y - 2 when distributed. Understanding how to properly distribute the negative sign is crucial for accurately simplifying the expression and avoiding errors in the final result.