Of course! Let's expand the expression [tex]\((3x - 1)^3\)[/tex].
To expand [tex]\((a - b)^3\)[/tex], we can use the binomial theorem, which states:
[tex]\[
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
\][/tex]
In this case, [tex]\(a = 3x\)[/tex] and [tex]\(b = 1\)[/tex]. Let's substitute these values into the formula:
1. Compute [tex]\(a^3\)[/tex]:
[tex]\[
(3x)^3 = 27x^3
\][/tex]
2. Compute [tex]\(-3a^2b\)[/tex]:
[tex]\[
-3 \cdot (3x)^2 \cdot 1 = -3 \cdot 9x^2 \cdot 1 = -27x^2
\][/tex]
3. Compute [tex]\(3ab^2\)[/tex]:
[tex]\[
3 \cdot (3x) \cdot 1^2 = 3 \cdot 3x \cdot 1 = 9x
\][/tex]
4. Compute [tex]\(-b^3\)[/tex]:
[tex]\[
-1^3 = -1
\][/tex]
Now, combine all these results:
[tex]\[
27x^3 - 27x^2 + 9x - 1
\][/tex]
Thus, the expanded form of [tex]\((3x - 1)^3\)[/tex] is:
[tex]\[
27x^3 - 27x^2 + 9x - 1
\][/tex]
