$\left(-3 x^2\right) \times 4 x \times(-x)$
Answer (2)
To simplify the expression ( − 3 x 2 ) × 4 x × ( − x ) , we first multiply the coefficients to get 12 and then combine the x terms to find x 4 . The final simplified expression is 12 x 4 .
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Multiply the coefficients: − 3 × 4 × − 1 = 12 .
Multiply the x terms: x 2 × x × x = x 4 .
Combine the results: 12 × x 4 = 12 x 4 .
The simplified expression is 12 x 4 .
Explanation
Understanding the Problem We are given the expression ( − 3 x 2 ) × 4 x × ( − x ) . Our goal is to simplify this expression by multiplying the coefficients and combining the x terms.
Multiplying the Coefficients First, let's multiply the coefficients: − 3 × 4 × − 1 . The product of − 3 and 4 is − 12 . Then, multiplying − 12 by − 1 gives us 12 .
Multiplying the x Terms Next, let's multiply the x terms: x 2 × x × x . When multiplying terms with the same base, we add the exponents. So, x 2 × x × x = x 2 + 1 + 1 = x 4 .
Combining the Results Now, we combine the results from the previous steps. We have the coefficient 12 and the x term x 4 . Therefore, the simplified expression is 12 x 4 .
Final Answer Thus, the simplified expression is 12 x 4 .
Examples
In physics, when calculating the kinetic energy of an object, you often deal with expressions involving mass and velocity squared. Simplifying such expressions is crucial for determining the energy accurately. For instance, if you have a scenario where the mass is related to x 2 and the velocity to x , simplifying their product helps in understanding the overall energy contribution. This type of algebraic simplification is also used in engineering to optimize designs and predict performance.
