Finite Math Examples

$(4 - j^{7}) (2 + j^{3})$

Step 1

Expand $(4 - j^{7}) (2 + j^{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 (2 + j^{3}) - j^{7} (2 + j^{3})$

Step 1.2

Apply the distributive property.

$4 \cdot 2 + 4 j^{3} - j^{7} (2 + j^{3})$

Step 1.3

Apply the distributive property.

$4 \cdot 2 + 4 j^{3} - j^{7} \cdot 2 - j^{7} j^{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $4$ by $2$ .

$8 + 4 j^{3} - j^{7} \cdot 2 - j^{7} j^{3}$

Step 2.2

Multiply $2$ by $- 1$ .

$8 + 4 j^{3} - 2 j^{7} - j^{7} j^{3}$

Step 2.3

Multiply $j^{7}$ by $j^{3}$ by adding the exponents.

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Step 2.3.1

Move $j^{3}$ .

$8 + 4 j^{3} - 2 j^{7} - (j^{3} j^{7})$

Step 2.3.2

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

$8 + 4 j^{3} - 2 j^{7} - j^{3 + 7}$

Step 2.3.3

Add $3$ and $7$ .

$8 + 4 j^{3} - 2 j^{7} - j^{10}$