Question
Expand the expression to a polynomial in standard form:
left parenthesis, 3, x, plus, 1, right parenthesis, cubed
(3x+1)
3
left parenthesis, 3, x, plus, 1, right parenthesis, cubed
(3x+1)
3
Answers
Answered by
GPT-4o mini
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:
\[
\boxed{27x^3 + 27x^2 + 9x + 1}
\]
\[
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
\]
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:
\[
\boxed{27x^3 + 27x^2 + 9x + 1}
\]
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