Converting from factored to standard form: why is this answer wrong?

Question

Converting the equation $$y=-2(x-2+\sqrt{5})(x-2-\sqrt{5})$$ to standard form seems to give $$-2x^{2\space }+3.528x+6.4171392.$$

My handout tells me that the answer is different. What is wrong here?

Answer 1

The decimal expansion suggests you used a calculator, and probably the error resulted from entering the quantity using the wrong order of operations. The factors in parentheses are the sum and difference of $x - 2$ and $\sqrt{5}$, so multiplying out the expression gives $$y = -2 ((x - 2)^2 - 5),$$ and in particular the standard form of the polynomial on the r.h.s. has integer coefficients.

Answer 2

$y = -2((x-2)^2 - 5) = -2(x^2-4x-1) = ....$