Multiply the monomials: $-11 x^2 y \text { and } 0.3 x^2 y^2$
Answer (2)
Multiply the coefficients: − 11 × 0.3 = − 3.3 .
Multiply the x terms: x 2 × x 2 = x 4 .
Multiply the y terms: y × y 2 = y 3 .
Combine the results: − 3.3 x 4 y 3 .
Explanation
Understanding the Problem We are asked to multiply two monomials: − 11 x 2 y and 0.3 x 2 y 2 . To do this, we will multiply the coefficients, multiply the x terms, and multiply the y terms.
Multiplying Coefficients First, let's multiply the coefficients: − 11 × 0.3 = − 3.3 .
Multiplying x Terms Next, let's multiply the x terms: x 2 × x 2 = x 2 + 2 = x 4 .
Multiplying y Terms Now, let's multiply the y terms: y × y 2 = y 1 + 2 = y 3 .
Combining the Results Finally, let's combine the results: − 3.3 x 4 y 3 .
Examples
Monomial multiplication is useful in various fields, such as physics and engineering, when dealing with polynomial expressions that represent physical quantities. For example, when calculating the area of a rectangle with sides expressed as monomials, multiplying these monomials gives the area in terms of a new monomial. This can help simplify complex calculations and provide a clear understanding of how different variables interact within a system. Understanding monomial multiplication provides a foundation for more advanced algebraic manipulations and problem-solving in real-world applications.
To multiply the monomials − 11 x 2 y and 0.3 x 2 y 2 , first multiply the coefficients to get − 3.3 . Then multiply the like terms: the x terms to get x 4 and the y terms to get y 3 . The final result is − 3.3 x 4 y 3 .
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