Expand the expression to a polynomial in standard form:

Question

left parenthesis, x, minus, 3, right parenthesis, cubed
(x−3)
3

Answer 1

To expand the expression \((x - 3)^3\), we can use the binomial theorem or perform the expansion step-by-step.

Using the binomial expansion formula \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\), we identify \(a = x\) and \(b = 3\):

\[ (x - 3)^3 = x^3 - 3(x^2)(3) + 3(x)(3^2) - 3^3 \]

Calculating each term:

1. \(x^3\)
2. \(-3(x^2)(3) = -9x^2\)
3. \(3(x)(3^2) = 3(x)(9) = 27x\)
4. \(-3^3 = -27\)

Now, combine these results:

\[ (x - 3)^3 = x^3 - 9x^2 + 27x - 27 \]

Thus, the expanded polynomial in standard form is:

\[ \boxed{x^3 - 9x^2 + 27x - 27} \]