Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 7r - 9r

Verified step by step guidance

1. Identify the common factor in the terms of the expression. Here, both terms have the variable \( r \).
2. Use the distributive property, which states that \( a b + a c = a(b + c) \), to factor out the common \( r \) from both terms: \( 7r - 9r = r(7 - 9) \).
3. Simplify the expression inside the parentheses by performing the subtraction: \( 7 - 9 \).
4. Rewrite the expression as \( r \) multiplied by the simplified result from the previous step.
5. If possible, write the final simplified expression by multiplying \( r \) by the simplified number.

Key Concepts

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually and then adding the products. In algebra, it is expressed as a(b + c) = ab + ac, allowing simplification of expressions by factoring or expanding.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 7r and -9r are like terms because both contain the variable r, so they can be combined by performing the arithmetic operation on their coefficients.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing all possible operations. This includes applying properties like distributive property and combining like terms to reduce the expression to a more manageable or recognizable form.