Question

What is the value of the expression a^2 + c^2 + 4ac + 4?

A) (a + c + 2)^2
B) (a + c - 2)^2
C) (a - c + 2)^2
D) (a - c - 2)^2

Answer 1

The value of the expression a^2 + c^2 + 4ac + 4 is (a + c + 2)^2 (Option A).

Step-by-step explanation:

The value of the expression a^2 + c^2 + 4ac + 4 is (a + c + 2)^2 (Option A).

To find this, we can factor the given expression. Starting with a^2 + c^2 + 4ac + 4, we notice that 4ac + 4 can be rewritten as 2(ac + 2). Rearranging terms, we get a^2 + 2ac + c^2 + 2(ac + 2). Now, we can combine like terms to obtain (a^2 + 2ac + c^2) + 2(ac + 2), which can be further simplified to (a + c)^2 + 2(ac + 2). Finally, (a + c)^2 + 2(ac + 2) can be rewritten as (a + c + 2)^2.