Final answer:
The expression (x + 7)^2 is simplified to x^2 + 14x + 49 by applying the square of a binomial formula, which is a correct application of algebraic simplification.
Step-by-step explanation:
To simplify the expression (x + 7)^2, we need to apply the square of a binomial formula, which is (a + b)^2 = a^2 + 2ab + b^2. Here, a would be x, and b would be 7. Following the formula:
- x^2: Squaring the first term x
- 2*x*7 = 14x: Multiplying the first term x by the second term 7 and doubling the product
- 7^2 = 49: Squaring the second term 7
Combining these, we get the simplified form x^2 + 14x + 49. Therefore, the correct answer is a) x^2 + 14x + 49.
It's important to eliminate terms wherever possible to simplify the algebra, and to check the answer to see if it is reasonable.