Calculus Examples

${(x - h)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$x^{3} + 3 \cdot - 1 x^{2} h + 3 x {(- h)}^{2} + {(- h)}^{3}$

Step 2.1.2

Multiply $3$ by $- 1$ .

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

Step 2.1.3

Apply the product rule to $- h$ .

$x^{3} - 3 x^{2} h + 3 x ({(- 1)}^{2} h^{2}) + {(- h)}^{3}$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$x^{3} - 3 x^{2} h + 3 \cdot {(- 1)}^{2} x h^{2} + {(- h)}^{3}$

Step 2.1.5

Raise $- 1$ to the power of $2$ .

$x^{3} - 3 x^{2} h + 3 \cdot 1 x h^{2} + {(- h)}^{3}$

Step 2.1.6

Multiply $3$ by $1$ .

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

Step 2.1.7

Apply the product rule to $- h$ .

$x^{3} - 3 x^{2} h + 3 x h^{2} + {(- 1)}^{3} h^{3}$

Step 2.1.8

Raise $- 1$ to the power of $3$ .

$x^{3} - 3 x^{2} h + 3 x h^{2} - h^{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $x^{2}$ .

$x^{3} - 3 h x^{2} + 3 x h^{2} - h^{3}$

Step 2.2.2

Move $x$ .

$x^{3} - 3 h x^{2} + 3 h^{2} x - h^{3}$

Step 2.2.3

Move $x^{3}$ .

$- 3 h x^{2} + 3 h^{2} x - h^{3} + x^{3}$

Step 2.2.4

Move $- 3 h x^{2}$ .

$3 h^{2} x - h^{3} - 3 h x^{2} + x^{3}$

Step 2.2.5

Reorder $3 h^{2} x$ and $- h^{3}$ .

$- h^{3} + 3 h^{2} x - 3 h x^{2} + x^{3}$