Simplify each expression. See Example 8. 10x (3)(y)

Verified step by step guidance

1. Identify the expression given: \$10x (3)(y)$, which involves multiplication of constants and variables.
2. Recall the associative property of multiplication, which allows us to rearrange and group factors without changing the product.
3. Group the constants together and the variables together: \((10 \times 3) \times (x \times y)\).
4. Multiply the constants: \(10 \times 3 = 30\).
5. Write the simplified expression as \$30xy$.

Key Concepts

Algebraic Simplification

Algebraic simplification involves combining like terms and applying arithmetic operations to rewrite expressions in a simpler form. In this case, it means multiplying constants and variables to reduce the expression to its simplest product.

Multiplication of Variables and Constants

When multiplying variables and constants, multiply the numerical coefficients together and write the variables as a product. For example, multiplying 10, 3, x, and y results in 30xy, combining all factors into one term.

Understanding Notation and Parentheses

Parentheses indicate grouping in expressions and clarify the order of operations. Recognizing that (3)(y) means 3 multiplied by y helps correctly interpret and simplify the expression by performing multiplication step-by-step.