Factor the expression x^2 + 10x + 25.

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Question: Factor the expression x^2 + 10x + 25.

Options:

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

Solution:

This is a perfect square trinomial. It can be factored as (x + 5)(x + 5) or (x + 5)^2.

Factor the expression x^2 + 10x + 25.

Factor the expression x^2 + 10x + 25.

Step 1: Identify the expression you want to factor, which is x^2 + 10x + 25.
Step 2: Look for a perfect square trinomial. A perfect square trinomial has the form (a + b)^2 = a^2 + 2ab + b^2.
Step 3: In the expression x^2 + 10x + 25, identify a and b. Here, a = x and b = 5 because 5^2 = 25.
Step 4: Check if the middle term (10x) is equal to 2ab. Calculate 2 * x * 5 = 10x, which matches the middle term.
Step 5: Since it matches, you can factor the expression as (x + 5)(x + 5).
Step 6: You can also write this as (x + 5)^2 to show it's a perfect square.

Perfect Square Trinomial – A trinomial of the form a^2 + 2ab + b^2 that can be factored into (a + b)^2.