Math Problem Statement

(5x^2 + 8) - (7x^2 - 5)

Solution

The problem provided asks to subtract two expressions:

(5x2+8)(7x25)(5x^2 + 8) - (7x^2 - 5)

Let's simplify this step by step.

Step 1: Distribute the negative sign

When subtracting, you distribute the negative sign to each term inside the parentheses:

(5x2+8)(7x25)=5x2+87x2+5(5x^2 + 8) - (7x^2 - 5) = 5x^2 + 8 - 7x^2 + 5

Step 2: Combine like terms

Now, combine the x2x^2 terms and the constants:

  • 5x27x2=2x25x^2 - 7x^2 = -2x^2
  • 8+5=138 + 5 = 13

Final result:

2x2+13-2x^2 + 13

So, the simplified expression is:

(5x2+8)(7x25)=2x2+13(5x^2 + 8) - (7x^2 - 5) = -2x^2 + 13

Let me know if you need further clarification or any additional details.

Here are 5 related questions to expand on this:

  1. How do you distribute a negative sign across an expression?
  2. Can you add or subtract terms with different powers of xx?
  3. What happens if both expressions have more variables?
  4. How do you handle similar subtraction problems with cubic terms, like x3x^3?
  5. What is the importance of like terms when simplifying expressions?

Tip: Always be careful with the signs when subtracting or distributing! Misplacing a negative can change the whole expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Operations
Combining Like Terms

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10