Answer: A. $(x+15)^2$

Explanation:1. Analyze the given expression: The expression is $(x+8)^2 + 14(x+8) + 49$.

2. Recognize the pattern of a perfect square trinomial: A perfect square trinomial has the form $A^2 + 2AB + B^2 = (A+B)^2$. Let $A = (x+8)$. Then the expression looks like $A^2 + 14A + 49$.

3. Check if $14A + 49$ fits the $2AB + B^2$ pattern with $A = (x+8)$: If the expression is $(A+B)^2$, then $A^2$ corresponds to $(x+8)^2$. $B^2$ corresponds to $49$. If $B^2 = 49$, then $B$ could be $7$ or $-7$. Let's test $B=7$. Then $2AB$ should correspond to $14(x+8)$. $2AB = 2(x+8)(7) = 14(x+8)$. This matches the middle term of the expression when $A = (x+8)$ and $B=7$.

4. Apply the perfect square trinomial formula: Since the expression is in the form $A^2 + 2AB + B^2$ with $A = (x+8)$ and $B=7$, it can be factored as $(A+B)^2$. Substitute back $A=(x+8)$ and $B=7$: $((x+8) + 7)^2$ $(x + 8 + 7)^2$ $(x + 15)^2$

5. Compare with the given options: [A] $(x+15)^2$ [B] $(x+7)^2$ [C] $8(x+7)^2$ [D] $7(x+8)^2$ Our result matches option A.

6. Conclusion: The expression equivalent to $(x+8)^2+14(x+8)+49$ is $(x+15)^2$.