Rewrite each expression using the distributive property and simplify, if possible. See Example 7. a + 7a

Verified step by step guidance

1. Identify the terms in the expression: \(a + 7a\) consists of two like terms involving \(a\).
2. Recall the distributive property: \(x + yx = (1 + y)x\), where \(x\) is a common factor.
3. Factor out the common variable \(a\) from both terms: \(a + 7a = (1 + 7)a\).
4. Simplify the expression inside the parentheses: \((1 + 7) = 8\).
5. Rewrite the expression as a single term: \$8a$.

Key Concepts

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend individually by the number and then adding the results. For example, a(b + c) = ab + ac. This property helps in rewriting expressions by factoring or expanding terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, a and 7a are like terms because both contain 'a'. Adding them results in 8a, simplifying the expression.

Algebraic Expressions

An algebraic expression consists of variables, constants, and operations. Understanding how to manipulate these expressions, such as factoring or simplifying, is essential for solving problems and rewriting expressions effectively.