Finite Math Examples

$- 3 r (r + s) (r + s)$

Step 1

Apply the distributive property.

$(- 3 r \cdot r - 3 r s) (r + s)$

Step 2

Multiply $r$ by $r$ by adding the exponents.

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Step 2.1

Move $r$ .

$(- 3 (r \cdot r) - 3 r s) (r + s)$

Step 2.2

Multiply $r$ by $r$ .

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

Step 3

Expand $(- 3 r^{2} - 3 r s) (r + s)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

$- 3 r^{2} r - 3 r^{2} s - 3 r s r - 3 r s \cdot s$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $r^{2}$ by $r$ by adding the exponents.

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Step 4.1.1.1

Move $r$ .

$- 3 (r \cdot r^{2}) - 3 r^{2} s - 3 r s r - 3 r s \cdot s$

Step 4.1.1.2

Multiply $r$ by $r^{2}$ .

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Step 4.1.1.2.1

Raise $r$ to the power of $1$ .

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

Step 4.1.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 r^{1 + 2} - 3 r^{2} s - 3 r s r - 3 r s \cdot s$

Step 4.1.1.3

Add $1$ and $2$ .

$- 3 r^{3} - 3 r^{2} s - 3 r s r - 3 r s \cdot s$

Step 4.1.2

Multiply $r$ by $r$ by adding the exponents.

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Step 4.1.2.1

Move $r$ .

$- 3 r^{3} - 3 r^{2} s - 3 (r \cdot r) s - 3 r s \cdot s$

Step 4.1.2.2

Multiply $r$ by $r$ .

$- 3 r^{3} - 3 r^{2} s - 3 r^{2} s - 3 r s \cdot s$

Step 4.1.3

Multiply $s$ by $s$ by adding the exponents.

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Step 4.1.3.1

Move $s$ .

$- 3 r^{3} - 3 r^{2} s - 3 r^{2} s - 3 r (s \cdot s)$

Step 4.1.3.2

Multiply $s$ by $s$ .

$- 3 r^{3} - 3 r^{2} s - 3 r^{2} s - 3 r s^{2}$

Step 4.2

Subtract $3 r^{2} s$ from $- 3 r^{2} s$ .

$- 3 r^{3} - 6 r^{2} s - 3 r s^{2}$