Linear Algebra Examples

$(4 w^{3} - 2 w^{2}) \cdot (10 w^{4})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$4 w^{3} (10 w^{4}) - 2 w^{2} (10 w^{4})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 10 w^{3} w^{4} - 2 w^{2} (10 w^{4})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 10 w^{3} w^{4} - 2 \cdot 10 w^{2} w^{4}$

Step 2

Simplify each term.

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Step 2.1

Multiply $w^{3}$ by $w^{4}$ by adding the exponents.

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Step 2.1.1

Move $w^{4}$ .

$4 \cdot 10 (w^{4} w^{3}) - 2 \cdot 10 w^{2} w^{4}$

Step 2.1.2

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

$4 \cdot 10 w^{4 + 3} - 2 \cdot 10 w^{2} w^{4}$

Step 2.1.3

Add $4$ and $3$ .

$4 \cdot 10 w^{7} - 2 \cdot 10 w^{2} w^{4}$

Step 2.2

Multiply $4$ by $10$ .

$40 w^{7} - 2 \cdot 10 w^{2} w^{4}$

Step 2.3

Multiply $w^{2}$ by $w^{4}$ by adding the exponents.

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Step 2.3.1

Move $w^{4}$ .

$40 w^{7} - 2 \cdot 10 (w^{4} w^{2})$

Step 2.3.2

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

$40 w^{7} - 2 \cdot 10 w^{4 + 2}$

Step 2.3.3

Add $4$ and $2$ .

$40 w^{7} - 2 \cdot 10 w^{6}$

Step 2.4

Multiply $- 2$ by $10$ .

$40 w^{7} - 20 w^{6}$