Math Problem Statement

(x - 5)( x + 5)

Solution

To simplify the expression (x5)(x+5)(x - 5)(x + 5), we can use the difference of squares formula, which states:

(ab)(a+b)=a2b2(a - b)(a + b) = a^2 - b^2

In this expression, a=xa = x and b=5b = 5. Applying the formula:

(x5)(x+5)=x252(x - 5)(x + 5) = x^2 - 5^2

Now calculate 525^2:

x225x^2 - 25

So, the simplified form of (x5)(x+5)(x - 5)(x + 5) is:

x225x^2 - 25

Would you like more details on this or have any questions?

Here are 5 related questions to explore further:

  1. How would you simplify the expression (x7)(x+7)(x - 7)(x + 7)?
  2. What is the expanded form of (x3)2(x - 3)^2?
  3. How can you factor the expression x236x^2 - 36?
  4. What happens when you multiply (x2)(x2)(x - 2)(x - 2)?
  5. How do you expand the product (2x5)(2x+5)(2x - 5)(2x + 5)?

Tip: When dealing with products of binomials that have the form (ab)(a+b)(a - b)(a + b), always consider using the difference of squares formula for quick simplification.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Difference of Squares

Formulas

Difference of squares: (a - b)(a + b) = a^2 - b^2

Theorems

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Suitable Grade Level

Grades 7-9