Basic Math Examples

$(4 i - 5) (4 i + 5)$

Step 1

Expand $(4 i - 5) (4 i + 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 i (4 i + 5) - 5 (4 i + 5)$

Step 1.2

Apply the distributive property.

$4 i (4 i) + 4 i \cdot 5 - 5 (4 i + 5)$

Step 1.3

Apply the distributive property.

$4 i (4 i) + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $4 i (4 i)$ .

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Step 2.1.1.1

Multiply $4$ by $4$ .

$16 i i + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.1.2

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

$16 (i^{1} i) + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.1.3

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

$16 (i^{1} i^{1}) + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.1.4

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

$16 i^{1 + 1} + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.1.5

Add $1$ and $1$ .

$16 i^{2} + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.2

Rewrite $i^{2}$ as $- 1$ .

$16 \cdot - 1 + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.3

Multiply $16$ by $- 1$ .

$- 16 + 4 i \cdot 5 - 5 (4 i) - 5 \cdot 5$

Step 2.1.4

Multiply $5$ by $4$ .

$- 16 + 20 i - 5 (4 i) - 5 \cdot 5$

Step 2.1.5

Multiply $4$ by $- 5$ .

$- 16 + 20 i - 20 i - 5 \cdot 5$

Step 2.1.6

Multiply $- 5$ by $5$ .

$- 16 + 20 i - 20 i - 25$

Step 2.2

Subtract $25$ from $- 16$ .

$- 41 + 20 i - 20 i$

Step 2.3

Subtract $20 i$ from $20 i$ .

$- 41 + 0$

Step 2.4

Add $- 41$ and $0$ .

$- 41$