Final answer:
The expression (x + 4)² is not equivalent to 2x² + 8x + 8; the correct expansion of (x + 4)² is x² + 8x + 16.
Step-by-step explanation:
The student has asked if the expression (x + 4)² is equivalent to 2x² + 8x + 8. The way to verify the equivalence is by expanding the squared term. When you multiply (x + 4) by itself, the correct expansion is:
(x + 4)(x + 4) = x² + 4x + 4x + 16 = x² + 8x + 16So, (x + 4)² is equivalent to x² + 8x + 16, and not 2x² + 8x + 8. Hence, the initial statement is incorrect because the coefficient of the x² term in the expanded form is 1, not 2, and the constant term is 16, not 8.