The equivalent expression to (x+4)^2 - (x-2)(x+4) is (x+4)[(x+4)-(x-2)], as it simplifies to 6x + 24, which matches the result of the provided expression.
To simplify the expression (x+4)^2 - (x-2)(x+4), let's first expand and then combine like terms:
(x+4)^2 expands to x^2 + 8x + 16, and (x-2)(x+4) expands to x^2 + 2x - 8.
Now, subtract the second expression from the first:
(x+4)^2 - (x-2)(x+4) = (x^2 + 8x + 16) - (x^2 + 2x - 8)
Combine like terms:
x^2 + 8x + 16 - x^2 - 2x + 8
Combine x^2 terms, x terms, and constants:
6x + 24
Now, let's compare the simplified expression 6x + 24 with the provided choices:
A. 4(x+4) is not equivalent.
B. 2(x+1)(x+4) is not equivalent.
C. (x+4)-(x-2) is not equivalent.
D. (x+4)[(x+4)-(x-2)] is equivalent.
Therefore, the expression equivalent to (x+4)^2 - (x-2)(x+4) is D. (x+4)[(x+4)-(x-2)].
The question probable may be:
Select the expression that is equivalent to (x+4)^2-(x-2)(x+4). A. 4(x+4) B. 2(x+1)(x+4) C. (x+4)-(x-2) D. (x+4)[(x+4)-(x-2)]