Calculus Examples

${(x + 2)}^{3} e^{- 3 x}$

Step 1

Use the Binomial Theorem.

$(x^{3} + 3 x^{2} \cdot 2 + 3 x \cdot 2^{2} + 2^{3}) e^{- 3 x}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2$ by $3$ .

$(x^{3} + 6 x^{2} + 3 x \cdot 2^{2} + 2^{3}) e^{- 3 x}$

Step 2.1.2

Raise $2$ to the power of $2$ .

$(x^{3} + 6 x^{2} + 3 x \cdot 4 + 2^{3}) e^{- 3 x}$

Step 2.1.3

Multiply $4$ by $3$ .

$(x^{3} + 6 x^{2} + 12 x + 2^{3}) e^{- 3 x}$

Step 2.1.4

Raise $2$ to the power of $3$ .

$(x^{3} + 6 x^{2} + 12 x + 8) e^{- 3 x}$

Step 2.2

Apply the distributive property.

$x^{3} e^{- 3 x} + 6 x^{2} e^{- 3 x} + 12 x e^{- 3 x} + 8 e^{- 3 x}$