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Chapter 1: Problem 17

\((x+1)^{3}\)

Short Answer

Expert verified
The expanded form of \((x+1)^{3}\) is \(x^3 + 3x^2 + 3x + 1.\)

Step by step solution

01

Identify the variables

In the equation \((x+1)^{3}\), identify a=x, b=1 and n=3.
02

Apply the Binomial Theorem

Using the binomial theorem formula \((x+1)^{3} = x^3 + \left(^3_1\right)x^{(3-1)}*1 + \left(^3_2\right)x^{(3-2)}*1^{2} + 1^{3}\), simplify the coefficients and get the second part of the equation which is \(1*x^2 + 3*x + 3*1 + 1.\)
03

Calculating the final solution

Simplify the equation to get the final result which equals to \(x^3 + 3x^2 + 3x + 1.\)

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