Question

expand the expression to a polynomial in standard form: (3x + 2)^3

Explanation:

Step1: Recall the binomial cube formula

The formula for \((a + b)^3\) is \(a^3 + 3a^2b + 3ab^2 + b^3\). Here, \(a = 3x\) and \(b = 2\).

Step2: Substitute \(a\) and \(b\) into the formula

First, calculate \(a^3=(3x)^3 = 27x^3\).
Then, \(3a^2b = 3\times(3x)^2\times2=3\times9x^2\times2 = 54x^2\).
Next, \(3ab^2=3\times(3x)\times(2)^2 = 3\times3x\times4 = 36x\).
Finally, \(b^3=(2)^3 = 8\).

Step3: Combine the terms

Add all the terms together: \(27x^3+54x^2 + 36x+8\).

Answer:

\(27x^3 + 54x^2 + 36x + 8\)