Factor the expression x^2 - 16.

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Question: Factor the expression x^2 - 16.

Options:

Correct Answer: (x - 4)(x + 4)

Solution:

This is a difference of squares. It can be factored as (x - 4)(x + 4).

Factor the expression x^2 - 16.

Factor the expression x^2 - 16.

Step 1: Identify the expression you want to factor, which is x^2 - 16.
Step 2: Recognize that this expression is a difference of squares. A difference of squares has the form a^2 - b^2.
Step 3: In this case, a^2 is x^2 (where a = x) and b^2 is 16 (where b = 4).
Step 4: Write the difference of squares formula: a^2 - b^2 = (a - b)(a + b).
Step 5: Substitute a and b into the formula: (x - 4)(x + 4).
Step 6: The factored form of the expression x^2 - 16 is (x - 4)(x + 4).

Difference of Squares – A mathematical identity that states a^2 - b^2 = (a - b)(a + b).