If $x=3$ and $y=-1$, evaluate $2(x^2-y^3)$.

Substitute x = 3 and y = − 1 into the expression 2 ( x 2 − y 3 ) .
Calculate x 2 = 3 2 = 9 and y 3 = ( − 1 ) 3 = − 1 .
Substitute the calculated values into the expression: 2 ( 9 − ( − 1 )) .
Simplify the expression: 2 ( 9 + 1 ) = 2 ( 10 ) = 20 . The final answer is 20 ​ .

Explanation

Understanding the Problem We are given the expression 2 ( x 2 − y 3 ) and the values x = 3 and y = − 1 . Our goal is to substitute these values into the expression and evaluate it.

Substitution First, we substitute the given values of x and y into the expression: 2 ( x 2 − y 3 ) = 2 (( 3 ) 2 − ( − 1 ) 3 ) .

Evaluating Exponents Next, we evaluate the exponents: ( 3 ) 2 = 3 × 3 = 9 and ( − 1 ) 3 = ( − 1 ) × ( − 1 ) × ( − 1 ) = − 1 .

Simplifying the Expression Now, we substitute these values back into the expression: 2 ( 9 − ( − 1 )) = 2 ( 9 + 1 ) .

Final Calculation Finally, we simplify the expression to obtain the final answer: 2 ( 10 ) = 20 .


Examples
Imagine you are calculating the energy of a system where the energy depends on two variables, x and y . The formula for the energy is given by 2 ( x 2 − y 3 ) . If you know that x = 3 and y = − 1 , you can substitute these values into the formula to find the energy of the system. This type of calculation is common in physics and engineering, where you often need to evaluate expressions by substituting known values for variables. For example, if x represents the velocity of an object and y represents its position, you can calculate the energy of the object at a specific velocity and position using this formula.

Answered by GinnyAnswer | 2025-07-05

To evaluate 2 ( x 2 − y 3 ) with x = 3 and y = − 1 , substitute and calculate to get the final result of 20.
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Answered by Anonymous | 2025-07-07