Simplifying (5x²)(3x)
This expression involves multiplying two monomials, where a monomial is a term with a coefficient and variables raised to non-negative integer exponents. Here's how to simplify it:
Understanding the Properties of Multiplication
- Commutative Property: The order of multiplication doesn't affect the result. So (5x²)(3x) is the same as (3x)(5x²).
- Associative Property: We can group the factors in any way we want. So (5x²)(3x) is the same as 5(x²)(3x).
Simplifying the Expression
- Group the coefficients and variables: 5(x²)(3x) = (5 * 3)(x² * x)
- Multiply the coefficients: (5 * 3)(x² * x) = 15(x² * x)
- Apply the product of powers rule: x² * x = x^(2+1) = x³
- Combine the results: 15(x² * x) = 15x³