Basic Math Examples

$h^{4} - {(h - g)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

$h^{4} - (h^{3} + 3 h^{2} (- g) + 3 h {(- g)}^{2} + {(- g)}^{3})$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$h^{4} - (h^{3} + 3 \cdot - 1 h^{2} g + 3 h {(- g)}^{2} + {(- g)}^{3})$

Step 1.2.2

Multiply $3$ by $- 1$ .

$h^{4} - (h^{3} - 3 h^{2} g + 3 h {(- g)}^{2} + {(- g)}^{3})$

Step 1.2.3

Apply the product rule to $- g$ .

$h^{4} - (h^{3} - 3 h^{2} g + 3 h ({(- 1)}^{2} g^{2}) + {(- g)}^{3})$

Step 1.2.4

Rewrite using the commutative property of multiplication.

$h^{4} - (h^{3} - 3 h^{2} g + 3 \cdot {(- 1)}^{2} h g^{2} + {(- g)}^{3})$

Step 1.2.5

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

$h^{4} - (h^{3} - 3 h^{2} g + 3 \cdot 1 h g^{2} + {(- g)}^{3})$

Step 1.2.6

Multiply $3$ by $1$ .

$h^{4} - (h^{3} - 3 h^{2} g + 3 h g^{2} + {(- g)}^{3})$

Step 1.2.7

Apply the product rule to $- g$ .

$h^{4} - (h^{3} - 3 h^{2} g + 3 h g^{2} + {(- 1)}^{3} g^{3})$

Step 1.2.8

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

$h^{4} - (h^{3} - 3 h^{2} g + 3 h g^{2} - g^{3})$

Step 1.3

Apply the distributive property.

$h^{4} - h^{3} - (- 3 h^{2} g) - (3 h g^{2}) - - g^{3}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $- 3$ by $- 1$ .

$h^{4} - h^{3} + 3 (h^{2} g) - (3 h g^{2}) - - g^{3}$

Step 1.4.2

Multiply $3$ by $- 1$ .

$h^{4} - h^{3} + 3 (h^{2} g) - 3 (h g^{2}) - - g^{3}$

Step 1.4.3

Multiply $- - g^{3}$ .

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Step 1.4.3.1

Multiply $- 1$ by $- 1$ .

$h^{4} - h^{3} + 3 (h^{2} g) - 3 (h g^{2}) + 1 g^{3}$

Step 1.4.3.2

Multiply $g^{3}$ by $1$ .

$h^{4} - h^{3} + 3 (h^{2} g) - 3 (h g^{2}) + g^{3}$

Step 1.5

Remove parentheses.

$h^{4} - h^{3} + 3 h^{2} g - 3 h g^{2} + g^{3}$

Step 2

Reorder.

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Step 2.1

Move $h^{2}$ .

$h^{4} - h^{3} + 3 g h^{2} - 3 h g^{2} + g^{3}$

Step 2.2

Move $h$ .

$h^{4} - h^{3} + 3 g h^{2} - 3 g^{2} h + g^{3}$

Step 2.3

Move $- h^{3}$ .

$h^{4} + 3 g h^{2} - 3 g^{2} h + g^{3} - h^{3}$

Step 2.4

Move $3 g h^{2}$ .

$h^{4} - 3 g^{2} h + g^{3} + 3 g h^{2} - h^{3}$

Step 2.5

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

$h^{4} + g^{3} - 3 g^{2} h + 3 g h^{2} - h^{3}$