Explanation:
among other details this is the main thing about the standard form :
a polynomial in standard form is the sum of one or more terms; each term must be a monomial in standard form. also, the degrees of the terms should be decreasing as much as possible from left to right.
a monomial is the product of one or more factors: a constant coefficient and one factor for each variable in the expression. via exponent (e.g. 0) we control which variable is actually "showing", as any x⁰ = 1 and can therefore be omitted when writing as factor.
in other words :
e.g.
4x³ + 2x² + 5x + 1
2x + 3y + 7xy
are examples of the standard form.
in our case we have only x a variable. but we need to do all the squaring and multiplications and summing up to get the standard form.
that means
2(x - 1)² - 2 = ...
remember the priorities :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
2(x - 1)² - 2 = 2(x² - 2x + 1) - 2 =
= 2x² - 4x + 2 - 2 = 2x² - 4x