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Chapter 0: Problem 51

Find each product. $$(x+1)^{3}$$

Short Answer

Expert verified
The product of \((x+1)^3\) is \(x^3+3x^2+3x+1\).

Step by step solution

01

Expand the Cubic Binomial

The given expression is a cubic binomial, meaning the entire expression \((x+1)\) is being cubed. Apply the binomial theorem which is \((a+b)^n = \sum_{k=0}^{n} {n \choose k} a^{n-k}b^k\). The expression \((x+1)^3\) translates to \((x+1)(x+1)(x+1)\). When expanded this becomes \(x^3+3x^2+3x+1\). The coefficients 1, 3, 3, 1 corresponds to the fourth row of the Pascal's Triangle, which is a simple way to determine coefficients in binomial expansions.
02

Final Simplification

Combine any like terms in the expression if applicable. However, in this case, \(x^3+3x^2+3x+1\) does not contain like terms, so the expression is already in its simplest form.

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