Final answer:
The statement provided is false because each side of the equation, when factored correctly, does result in the same expression. However, the initial un-factored form differs from the stated equation.
Step-by-step explanation:
The statement (x²+8x+16) · (x²-8x+16) = (x²-16)² is False. To verify this, we can factor both quadratic expressions on the left-hand side. The first expression, (x²+8x+16), is a perfect square trinomial which factors to (x+4)², and the second, (x²-8x+16), is also a perfect square trinomial factoring to (x-4)². Thus, the left-hand side of the equation becomes (x+4)²·(x-4)², which is the square of the difference of squares and can be written as ((x+4)(x-4))².
However, the right-hand side of the equation, (x²-16)², simplifies to (x²-4²)² which factored out is ((x+4)(x-4))². As we can see the factored forms of both sides are the same, but the initial statement given is not properly factored and hence the original statement is false. The correct form of the equation should thus be [(x+4)(x-4)]² = (x²-16)².