Simplify: $3 x \times 4 x^2$.
Answer (2)
Multiply the coefficients: 3 × 4 = 12 .
Multiply the variables: x × x 2 = x 1 + 2 = x 3 .
Combine the results: 12 x 3 .
The simplified expression is 12 x 3 .
Explanation
Understanding the Expression Let's simplify the expression 3 x × 4 x 2 . This involves multiplying the coefficients and adding the exponents of the variable x .
Multiplying Coefficients First, we multiply the coefficients: 3 × 4 = 12 .
Multiplying Variables with Exponents Next, we multiply the variables with their exponents: x × x 2 = x 1 + 2 = x 3 . Remember that when you multiply variables with exponents, you add the exponents. In this case, x is the same as x 1 , so we have x 1 × x 2 = x 1 + 2 = x 3 .
Combining the Results Finally, we combine the results from the previous steps: 12 x 3 . So, the simplified expression is 12 x 3 .
Final Answer Therefore, the simplified form of 3 x × 4 x 2 is 12 x 3 .
Examples
Understanding how to simplify expressions like 3 x × 4 x 2 is useful in many real-world situations. For example, if you are calculating the area of a rectangle where the length is 4 x 2 and the width is 3 x , the area would be 3 x × 4 x 2 = 12 x 3 . Similarly, in physics, if you are dealing with quantities that vary with powers of a variable, simplifying expressions becomes essential for making calculations and predictions. This skill is also crucial in engineering, computer science, and economics, where mathematical models often involve polynomial expressions.
The expression 3 x × 4 x 2 simplifies to 12 x 3 by multiplying the coefficients and adding the exponents of the variable. The final result is 12 x 3 .
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