Answer:
Standard form = 6x^2 - 5x + 1
Explanation:
Currently, (2x - 1)(3x - 1) is in factored, whose general equation is given by:
f(x) = a(x - r)(x - s), where
- a is a constant determining if the parabola opens up or down,
- and r and s are the factors.
The general equation of the standard form is given by:
f(x) = ax^2 + bx + c.
Thus, we can convert from factored to standard form using the FOIL method where:
- F refers to the first terms (2x and 3x),
- O refers to the outer terms (2x and -1),
- I refers to the inner terms (-1 and 3x),
- and L refers to the last terms (-1 and -1).
We multiply the first, outer, inner, and last terms and simplify at the end:
(2x * 3x) + (2x * -1) + (-1 * 3x) + (-1 * -1)
6x^2 - 2x - 3x + 1
6x^2 - 5x + 1
Thus, the standard form of the quadratic expression (2x - 1)(3x - 1) is 6x^2 - 5x + 1.