Basic Math Examples

{(r - h)}^{3}

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

Step 1

Use the Binomial Theorem.

r^{3} + 3 r^{2} (- h) + 3 r {(- h)}^{2} + {(- h)}^{3}

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

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.

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

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

Step 2.1.2

Multiply

3

$3$ by

- 1

$- 1$ .

r^{3} - 3 r^{2} h + 3 r {(- h)}^{2} + {(- h)}^{3}

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

Step 2.1.3

Apply the product rule to

- h

$- h$ .

r^{3} - 3 r^{2} h + 3 r ({(- 1)}^{2} h^{2}) + {(- h)}^{3}

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

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

Step 2.1.5

Raise

- 1

$- 1$ to the power of

2

$2$ .

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

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

Step 2.1.6

Multiply

3

$3$ by

1

$1$ .

r^{3} - 3 r^{2} h + 3 r h^{2} + {(- h)}^{3}

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

Step 2.1.7

Apply the product rule to

- h

$- h$ .

r^{3} - 3 r^{2} h + 3 r h^{2} + {(- 1)}^{3} h^{3}

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

Step 2.1.8

Raise

- 1

$- 1$ to the power of

3

$3$ .

r^{3} - 3 r^{2} h + 3 r h^{2} - h^{3}

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

r^{3} - 3 r^{2} h + 3 r h^{2} - h^{3}

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Move

r^{2}

$r^{2}$ .

r^{3} - 3 h r^{2} + 3 r h^{2} - h^{3}

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

Step 2.2.2

Move

r

$r$ .

r^{3} - 3 h r^{2} + 3 h^{2} r - h^{3}

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

Step 2.2.3

Move

r^{3}

$r^{3}$ .

- 3 h r^{2} + 3 h^{2} r - h^{3} + r^{3}

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

Step 2.2.4

Move

- 3 h r^{2}

$- 3 h r^{2}$ .

3 h^{2} r - h^{3} - 3 h r^{2} + r^{3}

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

Step 2.2.5

Reorder

$3 h^{2} r$ and

$- h^{3}$ .

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