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

Verified step by step guidance

1. Identify the terms in the expression: here, both terms are \( x \) and \( x \).
2. Recognize that the distributive property allows you to factor out the common term \( x \) from both terms.
3. Rewrite the expression using the distributive property: \( x + x = x \times 1 + x \times 1 \).
4. Factor out \( x \) from both terms: \( x \times (1 + 1) \).
5. Simplify inside the parentheses: \( 1 + 1 = 2 \), so the expression becomes \( x \times 2 \) or \( 2x \).

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. For example, a(b + c) = ab + ac. This property helps simplify 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, x + x can be combined as 2x because both terms are like terms with the variable x.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing operations such as addition, subtraction, multiplication, or division. Simplifying expressions makes them easier to understand and work with in further calculations.