Evaluate the expression for $x=4$ and $y=5$.
$6\left(x^2-y\right)-y^2$
A. 8
B. 41
C. 47
D. 56
Answer (1)
Substitute x = 4 and y = 5 into the expression 6 ( x 2 − y ) − y 2 .
Calculate 4 2 = 16 and substitute: 6 ( 16 − 5 ) − 5 2 .
Simplify inside the parentheses: 6 ( 11 ) − 5 2 .
Evaluate: 66 − 25 = 41 .
Explanation
Understanding the problem We are asked to evaluate the expression 6 ( x 2 − y ) − y 2 for x = 4 and y = 5 . We will substitute these values into the expression and simplify to find the answer.
Substitution First, substitute x = 4 and y = 5 into the expression: 6 ( 4 2 − 5 ) − 5 2
Calculating 4 2 Next, we evaluate 4 2 which is 4 × 4 = 16 . So the expression becomes: 6 ( 16 − 5 ) − 5 2
Simplifying inside parentheses Now, we simplify the expression inside the parentheses: 16 − 5 = 11 . Thus, the expression is: 6 ( 11 ) − 5 2
Calculating 6 × 11 Then, we calculate 6 × 11 = 66 . The expression is now: 66 − 5 2
Calculating 5 2 Next, we evaluate 5 2 which is 5 × 5 = 25 . So the expression becomes: 66 − 25
Final Calculation Finally, we subtract 25 from 66: 66 − 25 = 41 . Therefore, the value of the expression is 41.
Conclusion The value of the expression 6 ( x 2 − y ) − y 2 when x = 4 and y = 5 is 41.
Examples
Imagine you are calculating the profit of a small business. Let's say 'x' represents the number of products sold and 'y' represents the fixed costs. The expression might represent the total revenue minus costs. By substituting the values of 'x' and 'y', you can quickly determine the profit for a specific scenario. This kind of calculation is fundamental in business to understand financial performance and make informed decisions.
