Answer: x^2 + 4x + 4 factors to (x + 2)^2.
Step-by-step explanation:
To factor the expression x^2 + 4x + 4, we can follow these steps:
1. Identify the factors of the constant term (4) that add up to the coefficient of the x-term (4). In this case, both factors are 2 since 2 * 2 = 4 and 2 + 2 = 4.
2. Rewrite the expression using these factors:
x^2 + 2x + 2x + 4
3. Group the terms in pairs:
(x^2 + 2x) + (2x + 4)
4. Factor out the greatest common factor from each pair:
x(x + 2) + 2(x + 2)
5. Notice that both terms now have a common factor of (x + 2). Factor out this common binomial:
(x + 2)(x + 2)
6. Simplify to get the final factored form:
(x + 2)^2
Therefore, x^2 + 4x + 4 factors to (x + 2)^2.
