(5x%5E4y%5E4).jpeg "(-3xy^3)(5x^4y^4)")
Multiplying Monomials: (-3xy^3)(5x^4y^4)
This article will guide you through multiplying the monomials (-3xy^3) and (5x^4y^4).
Understanding Monomials
Monomials are algebraic expressions consisting of a single term. They are formed by multiplying constants and variables raised to non-negative integer powers. In this case, both (-3xy^3) and (5x^4y^4) are monomials.
The Multiplication Process
To multiply monomials, we follow these simple steps:
- Multiply the coefficients: In our case, the coefficients are -3 and 5. Their product is -15.
- Multiply the variables: We multiply the variables by adding their exponents. For 'x', we have x¹ * x⁴ = x⁵. For 'y', we have y³ * y⁴ = y⁷.
- Combine the results: Combining the results from steps 1 and 2, we get -15x⁵y⁷.
The Solution
Therefore, the product of (-3xy³) and (5x⁴y⁴) is -15x⁵y⁷.
Key Takeaways
- Multiplying monomials involves multiplying the coefficients and adding the exponents of variables with the same base.
- Remember that a negative coefficient multiplied by a positive coefficient results in a negative coefficient.