Factor the expression x^2 - 25.

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Question: Factor the expression x^2 - 25.

Options:

Correct Answer: (x - 5)(x + 5)

Solution:

Using the difference of squares identity, x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5).

Factor the expression x^2 - 25.

Factor the expression x^2 - 25.

Step 1: Identify the expression you want to factor, which is x^2 - 25.
Step 2: Recognize that 25 is a perfect square because it can be written as 5^2.
Step 3: Rewrite the expression using the perfect square: x^2 - 25 = x^2 - 5^2.
Step 4: Apply the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b). Here, a is x and b is 5.
Step 5: Substitute a and b into the formula: (x - 5)(x + 5).
Step 6: Write the final factored form: x^2 - 25 = (x - 5)(x + 5).

Difference of Squares – The difference of squares identity states that a^2 - b^2 can be factored into (a - b)(a + b).