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(2x^2)(3x^3)

2 min read Jun 16, 2024
(2x^2)(3x^3)

Multiplying Monomials: (2x^2)(3x^3)

This article will guide you through the steps of multiplying the monomials (2x^2) and (3x^3).

Understanding Monomials

A monomial is a single term algebraic expression consisting of a coefficient and one or more variables raised to non-negative integer powers.

For example, in the monomial 2x^2:

  • 2 is the coefficient.
  • x is the variable.
  • 2 is the exponent.

Multiplication of Monomials

To multiply monomials, we follow these steps:

  1. Multiply the coefficients: In our case, we multiply 2 and 3, which gives us 6.

  2. Multiply the variables: We multiply x^2 and x^3. Remember that when multiplying variables with exponents, we add the exponents. So, x^2 * x^3 = x^(2+3) = x^5

  3. Combine the results: Combining the results from steps 1 and 2, we get 6x^5.

Therefore, (2x^2)(3x^3) = 6x^5.

Key Points

  • Multiplication of coefficients: Multiply the numerical coefficients together.
  • Addition of exponents: When multiplying variables with exponents, add the exponents together.
  • Simplifying the expression: Combine the results to obtain the final answer.

By applying these steps, we can confidently multiply any pair of monomials.

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