Multiply (x-h)^3 - MathMaster

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

Use the Binomial Theorem.

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

Simplify terms.

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Simplify each term.

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Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $- 1$ .

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

Apply the product rule to $- h$ .

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

Rewrite using the commutative property of multiplication.

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

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

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

Multiply $3$ by $1$ .

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

Apply the product rule to $- h$ .

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

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

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

Simplify the expression.

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Move $x^{2}$ .

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

Move $x$ .

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

Move $x^{3}$ .

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

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

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

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

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

Multiply (x-h)^3

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