In Exercises 117–130, simplify each algebraic expression. 5(3y-2)-(7y+2)

Verified step by step guidance

1. Distribute the 5 across the terms inside the parentheses: $5(3y-2)$ becomes $15y-10$.
2. Rewrite the expression with the distributed terms: $15y-10-(7y+2)$.
3. Distribute the negative sign across the terms inside the second parentheses: $-(7y+2)$ becomes $-7y-2$.
4. Combine like terms: $15y-7y$ and $-10-2$.
5. Simplify the expression by performing the addition and subtraction: $(15y-7y)+(-10-2)$.

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 parenthesis. In the given expression, applying the distributive property is essential to simplify the terms correctly before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying algebraic expressions, as it helps to consolidate the expression into a more manageable form. In the provided expression, after distributing, identifying and combining like terms will lead to the final simplified result.

Negative Sign Distribution

When a negative sign is in front of a parenthesis, it must be distributed to each term inside the parenthesis. This means that each term will change its sign when simplified. In the expression given, correctly applying this concept is vital to ensure that all terms are accurately accounted for in the simplification process.