Factor the expression 4x² - 25.

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Question: Factor the expression 4x² - 25.

Options:

Correct Answer: (2x - 5)(2x + 5)

Solution:

4x² - 25 = (2x - 5)(2x + 5) as it is a difference of squares.

Factor the expression 4x² - 25.

Factor the expression 4x² - 25.

Step 1: Identify the expression you want to factor, which is 4x² - 25.
Step 2: Recognize that this expression is a difference of squares. A difference of squares has the form a² - b².
Step 3: Rewrite 4x² as (2x)² and 25 as 5². So, we have (2x)² - 5².
Step 4: Use the difference of squares formula, which states that a² - b² = (a - b)(a + b).
Step 5: Apply the formula: Here, a = 2x and b = 5. So, we get (2x - 5)(2x + 5).
Step 6: Write the final factored form: 4x² - 25 = (2x - 5)(2x + 5).

Difference of Squares – The expression is a difference of squares, which can be factored using the formula a² - b² = (a - b)(a + b).