Basic Math Examples

$3 - 5 {(w + q)}^{2} + {(w + q)}^{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(w + q)}^{2}$ as $(w + q) (w + q)$ .

$3 - 5 ((w + q) (w + q)) + {(w + q)}^{3}$

Step 1.2

Expand $(w + q) (w + q)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 - 5 (w (w + q) + q (w + q)) + {(w + q)}^{3}$

Step 1.2.2

Apply the distributive property.

$3 - 5 (w \cdot w + w q + q (w + q)) + {(w + q)}^{3}$

Step 1.2.3

Apply the distributive property.

$3 - 5 (w \cdot w + w q + q w + q \cdot q) + {(w + q)}^{3}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $w$ by $w$ .

$3 - 5 (w^{2} + w q + q w + q \cdot q) + {(w + q)}^{3}$

Step 1.3.1.2

Multiply $q$ by $q$ .

$3 - 5 (w^{2} + w q + q w + q^{2}) + {(w + q)}^{3}$

Step 1.3.2

Add $w q$ and $q w$ .

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Step 1.3.2.1

Reorder $w$ and $q$ .

$3 - 5 (w^{2} + q w + q w + q^{2}) + {(w + q)}^{3}$

Step 1.3.2.2

Add $q w$ and $q w$ .

$3 - 5 (w^{2} + 2 q w + q^{2}) + {(w + q)}^{3}$

Step 1.4

Apply the distributive property.

$3 - 5 w^{2} - 5 (2 q w) - 5 q^{2} + {(w + q)}^{3}$

Step 1.5

Multiply $2$ by $- 5$ .

$3 - 5 w^{2} - 10 (q w) - 5 q^{2} + {(w + q)}^{3}$

Step 1.6

Use the Binomial Theorem.

$3 - 5 w^{2} - 10 q w - 5 q^{2} + w^{3} + 3 w^{2} q + 3 w q^{2} + q^{3}$

Step 2

Simplify the expression.

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Step 2.1

Move $w^{2}$ .

$3 - 5 w^{2} - 10 q w - 5 q^{2} + w^{3} + 3 q w^{2} + 3 w q^{2} + q^{3}$

Step 2.2

Move $w$ .

$3 - 5 w^{2} - 10 q w - 5 q^{2} + w^{3} + 3 q w^{2} + 3 q^{2} w + q^{3}$

Step 2.3

Move $3$ .

$- 5 w^{2} - 10 q w - 5 q^{2} + w^{3} + 3 q w^{2} + 3 q^{2} w + q^{3} + 3$

Step 2.4

Move $- 5 w^{2}$ .

$- 10 q w - 5 q^{2} + w^{3} + 3 q w^{2} + 3 q^{2} w + q^{3} - 5 w^{2} + 3$

Step 2.5

Move $- 10 q w$ .

$- 5 q^{2} + w^{3} + 3 q w^{2} + 3 q^{2} w + q^{3} - 10 q w - 5 w^{2} + 3$

Step 2.6

Move $- 5 q^{2}$ .

$w^{3} + 3 q w^{2} + 3 q^{2} w + q^{3} - 5 q^{2} - 10 q w - 5 w^{2} + 3$

Step 2.7

Move $w^{3}$ .

$3 q w^{2} + 3 q^{2} w + q^{3} + w^{3} - 5 q^{2} - 10 q w - 5 w^{2} + 3$

Step 2.8

Move $3 q w^{2}$ .

$3 q^{2} w + q^{3} + 3 q w^{2} + w^{3} - 5 q^{2} - 10 q w - 5 w^{2} + 3$

Step 2.9

Reorder $3 q^{2} w$ and $q^{3}$ .

$q^{3} + 3 q^{2} w + 3 q w^{2} + w^{3} - 5 q^{2} - 10 q w - 5 w^{2} + 3$