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Chapter 0: Problem 52

Find each product. $$(x+2)^{3}$$

Short Answer

Expert verified
\((x+2)^{3}\) expands to \(x^3 + 6x^2 + 12x + 8\).

Step by step solution

01

Expand the Expression

\((x+2)^{3}\) can be written as \((x+2) * (x+2) * (x+2)\). Let's expand this step by step. First, we expand the first two brackets: \((x+2) * (x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4\).
02

Multiply with Third Bracket

Now, the result \((x^2 + 4x + 4)\) is multiplied with the third bracket \((x+2)\). This gives us: \(x^3 + 4x^2 + 4x + 2x^2 + 8x + 8 + 2x^3 + 8x^2 + 8x = x^3 + 6x^2 + 12x + 8\).

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