Math Problem Statement

Solution

The expression X216X^2 - 16 is a difference of squares. The difference of squares can be factored using the formula:

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

In this case, X2X^2 is a2a^2 and 1616 is b2b^2. So we can identify a=Xa = X and b=4b = 4 because 42=164^2 = 16.

Applying the difference of squares formula, we get:

X216=(X+4)(X4)X^2 - 16 = (X + 4)(X - 4)

Thus, the factors of the expression X216X^2 - 16 are:

A. (X+4)(X4)\boxed{\text{A. } (X + 4)(X - 4)}

Do you want details or have any questions? Here are five more questions you might ask:

  1. How do you factor expressions using the difference of squares formula?
  2. What are other common factoring formulas for polynomials?
  3. How do you factor trinomials of the form ax2+bx+cax^2 + bx + c?
  4. What is the process for factoring by grouping?
  5. How can you verify that your factored form of a polynomial is correct?

Tip: When factoring polynomials, always check if the expression can be written as a difference of squares, a perfect square trinomial, or if common factors can be factored out first.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Factoring

Formulas

Difference of squares formula

Theorems

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Suitable Grade Level

Grades 9-12