Factor the expression: 4x^2 - 25.

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Question: Factor the expression: 4x^2 - 25.

Options:

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

Solution:

The expression 4x^2 - 25 is a difference of squares. It can be factored as (2x - 5)(2x + 5).

Factor the expression: 4x^2 - 25.

Factor the expression: 4x^2 - 25.

Step 1: Identify the expression you want to factor, which is 4x^2 - 25.
Step 2: Recognize that this expression is a difference of squares. A difference of squares has the form a^2 - b^2.
Step 3: Rewrite 4x^2 as (2x)^2 because (2x) * (2x) = 4x^2.
Step 4: Rewrite 25 as 5^2 because 5 * 5 = 25.
Step 5: Now, the expression looks like (2x)^2 - 5^2, which is a difference of squares.
Step 6: Use the difference of squares formula: a^2 - b^2 = (a - b)(a + b). Here, a = 2x and b = 5.
Step 7: Apply the formula: (2x - 5)(2x + 5).

Difference of Squares – A mathematical identity that states a^2 - b^2 = (a - b)(a + b), used to factor expressions that are the difference of two squares.