Basic Math Examples

$(3 k^{2} + 4 m) (2 k + 5 m^{3})$

Step 1

Expand $(3 k^{2} + 4 m) (2 k + 5 m^{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 k^{2} (2 k + 5 m^{3}) + 4 m (2 k + 5 m^{3})$

Step 1.2

Apply the distributive property.

$3 k^{2} (2 k) + 3 k^{2} (5 m^{3}) + 4 m (2 k + 5 m^{3})$

Step 1.3

Apply the distributive property.

$3 k^{2} (2 k) + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

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.

$3 \cdot 2 k^{2} k + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.2

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

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Step 2.1.2.1

Move $k$ .

$3 \cdot 2 (k \cdot k^{2}) + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$3 \cdot 2 (k^{1} k^{2}) + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.2.2.2

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

$3 \cdot 2 k^{1 + 2} + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.2.3

Add $1$ and $2$ .

$3 \cdot 2 k^{3} + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.3

Multiply $3$ by $2$ .

$6 k^{3} + 3 k^{2} (5 m^{3}) + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$6 k^{3} + 3 \cdot 5 k^{2} m^{3} + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.5

Multiply $3$ by $5$ .

$6 k^{3} + 15 k^{2} m^{3} + 4 m (2 k) + 4 m (5 m^{3})$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$6 k^{3} + 15 k^{2} m^{3} + 4 \cdot 2 m k + 4 m (5 m^{3})$

Step 2.1.7

Multiply $4$ by $2$ .

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 m (5 m^{3})$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 \cdot 5 m \cdot m^{3}$

Step 2.1.9

Multiply $m$ by $m^{3}$ by adding the exponents.

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Step 2.1.9.1

Move $m^{3}$ .

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 \cdot 5 (m^{3} m)$

Step 2.1.9.2

Multiply $m^{3}$ by $m$ .

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Step 2.1.9.2.1

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

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 \cdot 5 (m^{3} m^{1})$

Step 2.1.9.2.2

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

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 \cdot 5 m^{3 + 1}$

Step 2.1.9.3

Add $3$ and $1$ .

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 4 \cdot 5 m^{4}$

Step 2.1.10

Multiply $4$ by $5$ .

$6 k^{3} + 15 k^{2} m^{3} + 8 m k + 20 m^{4}$

Step 2.2

Reorder.

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Step 2.2.1

Move $m$ .

$6 k^{3} + 15 k^{2} m^{3} + 8 k m + 20 m^{4}$

Step 2.2.2

Move $8 k m$ .

$6 k^{3} + 15 k^{2} m^{3} + 20 m^{4} + 8 k m$

Step 2.2.3

Move $6 k^{3}$ .

$15 k^{2} m^{3} + 20 m^{4} + 6 k^{3} + 8 k m$