Let's write the quadratic equation [tex]\((x - 3)^2\)[/tex] in standard form. The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are constants.
1. Start with the given equation:
[tex]\[
(x - 3)^2 = 0
\][/tex]
2. Expand the expression [tex]\((x - 3)^2\)[/tex]:
[tex]\[
(x - 3)(x - 3)
\][/tex]
3. Apply the distributive property (also known as the FOIL method for binomials) to expand the expression:
[tex]\[
(x - 3)(x - 3) = x^2 - 3x - 3x + 9
\][/tex]
4. Combine like terms:
[tex]\[
x^2 - 3x - 3x + 9 = x^2 - 6x + 9
\][/tex]
Therefore, the quadratic equation in standard form is:
[tex]\[
x^2 - 6x + 9 = 0
\][/tex]
