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

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Identify the expression given: \$10x (3)(y)$. This involves multiplication of constants and variables.

Rewrite the expression by grouping the constants and variables separately: $(10 \times 3) \times (x \times y)$.

Multiply the constants together: $10 \times 3 = 30$.

Combine the variables by multiplication: $x \times y = xy$.

Write the simplified expression by combining the results: \$30xy$.

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Algebraic Simplification

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

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Algebraic Operations on Vectors

Multiplication of Variables and Constants

When multiplying variables and constants, multiply the numerical coefficients and then write the variables together. For example, multiplying 10x by 3y involves multiplying 10 and 3 to get 30, and then combining the variables x and y as xy.

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Equations with Two Variables

Understanding Notation and Expression Structure

Recognizing how expressions are written, such as 10x(3)(y), helps in correctly applying operations. Parentheses indicate multiplication, so the expression means 10 times x times 3 times y, which guides the order and method of simplification.

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