Multiply (7y) [tex] \left(-3 y^2\right) [/tex]
A. [tex] -73 y^3 [/tex]
B. [tex] 63 y^3 [/tex]
C. [tex] -21 y^3 [/tex]
D. [tex] 4 y^2 [/tex]
Answer (1)
Multiply the coefficients: 7 × − 3 = − 21 .
Multiply the variables: y × y 2 = y 3 .
Combine the results: − 21 y 3 .
The final answer is − 21 y 3 .
Explanation
Understanding the problem Let's multiply the given expression ( 7 y ) × ( − 3 y 2 ) .
Multiplying the coefficients First, we multiply the coefficients: 7 × − 3 = − 21 .
Multiplying the variables Next, we multiply the variables: y × y 2 = y 1 + 2 = y 3 .
Combining the results Now, we combine the results: − 21 y 3 .
Final Answer Comparing our result with the given options, we see that the correct answer is − 21 y 3 .
Examples
Understanding polynomial multiplication is crucial in various fields like physics and engineering, where it helps in modeling complex systems. For example, when calculating the trajectory of a projectile, you often need to multiply polynomial expressions to determine its position at a given time. Similarly, in electrical engineering, polynomial multiplication is used to analyze circuits and design filters. Mastering these algebraic manipulations provides a strong foundation for tackling real-world problems in science and technology.
