Math Problem Statement

Evaluate the expression x^2 - y(x + y) with x = 8 and y = 1.5.

Solution

The expression given is:

x2y(x+y)x^2 - y(x + y)

with the values x=8x = 8 and y=1.5y = 1.5.

Let's substitute these values into the expression and solve:

  1. Substitute x=8x = 8 and y=1.5y = 1.5: 821.5(8+1.5)8^2 - 1.5(8 + 1.5)

  2. Calculate 828^2: 82=648^2 = 64

  3. Calculate 8+1.58 + 1.5: 8+1.5=9.58 + 1.5 = 9.5

  4. Multiply yy with (x+y)(x + y): 1.5×9.5=14.251.5 \times 9.5 = 14.25

  5. Subtract this result from x2x^2: 6414.25=49.7564 - 14.25 = 49.75

So, the final answer is:

49.7549.75

Would you like more details or have any questions?

Here are some related questions you might find useful:

  1. How would the result change if we altered the values of xx and yy?
  2. Can this expression be simplified further before substituting values?
  3. What happens if we set y=0y = 0? How does it affect the expression?
  4. How can we generalize the solution for any values of xx and yy?
  5. What is the significance of solving such an expression in real-world applications?

Tip: Always perform operations inside parentheses first to ensure accuracy in complex expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Basic Arithmetic

Formulas

Expression Evaluation

Theorems

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Suitable Grade Level

Grades 6-8