Expand the expression to a polynomial in standard form:

Question

left parenthesis, 3, x, plus, 1, right parenthesis, cubed
(3x+1)
3

Answer 1

To expand the expression \((3x + 1)^3\), we can use the binomial theorem or apply the formula for the cube of a binomial. The general formula for \((a + b)^3\) is:

\[ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \]

In this case, let \(a = 3x\) and \(b = 1\).

Now we can expand:

1. Calculate \(a^3\): \[ (3x)^3 = 27x^3 \]

2. Calculate \(3a^2b\): \[ 3(3x)^2(1) = 3 \cdot 9x^2 \cdot 1 = 27x^2 \]

3. Calculate \(3ab^2\): \[ 3(3x)(1^2) = 3 \cdot 3x \cdot 1 = 9x \]

4. Calculate \(b^3\): \[ 1^3 = 1 \]

Now combine all the terms together: \[ (3x + 1)^3 = 27x^3 + 27x^2 + 9x + 1 \]

Thus, the expression \((3x + 1)^3\) expanded and written in standard form is:

\[ \boxed{27x^3 + 27x^2 + 9x + 1} \]