Finite Math Examples

$(x + 5 i) (x - 5 i) (x - 3)$

Step 1

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

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Step 1.1

Apply the distributive property.

$(x (x - 5 i) + 5 i (x - 5 i)) (x - 3)$

Step 1.2

Apply the distributive property.

$(x \cdot x + x (- 5 i) + 5 i (x - 5 i)) (x - 3)$

Step 1.3

Apply the distributive property.

$(x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)) (x - 3)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x \cdot x + x (- 5 i) + 5 i x + 5 i (- 5 i)$ .

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Step 2.1.1

Reorder the factors in the terms $x (- 5 i)$ and $5 i x$ .

$(x \cdot x - 5 i x + 5 i x + 5 i (- 5 i)) (x - 3)$

Step 2.1.2

Add $- 5 i x$ and $5 i x$ .

$(x \cdot x + 0 + 5 i (- 5 i)) (x - 3)$

Step 2.1.3

Add $x \cdot x$ and $0$ .

$(x \cdot x + 5 i (- 5 i)) (x - 3)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

$(x^{2} + 5 i (- 5 i)) (x - 3)$

Step 2.2.2

Multiply $5 i (- 5 i)$ .

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Step 2.2.2.1

Multiply $- 5$ by $5$ .

$(x^{2} - 25 i i) (x - 3)$

Step 2.2.2.2

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

$(x^{2} - 25 (i^{1} i)) (x - 3)$

Step 2.2.2.3

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

$(x^{2} - 25 (i^{1} i^{1})) (x - 3)$

Step 2.2.2.4

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

$(x^{2} - 25 i^{1 + 1}) (x - 3)$

Step 2.2.2.5

Add $1$ and $1$ .

$(x^{2} - 25 i^{2}) (x - 3)$

Step 2.2.3

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

$(x^{2} - 25 \cdot - 1) (x - 3)$

Step 2.2.4

Multiply $- 25$ by $- 1$ .

$(x^{2} + 25) (x - 3)$

Step 3

Expand $(x^{2} + 25) (x - 3)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$x^{2} (x - 3) + 25 (x - 3)$

Step 3.2

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 3 + 25 (x - 3)$

Step 3.3

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 3 + 25 x + 25 \cdot - 3$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

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

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Step 4.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 3 + 25 x + 25 \cdot - 3$

Step 4.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 3 + 25 x + 25 \cdot - 3$

Step 4.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 3 + 25 x + 25 \cdot - 3$

Step 4.2

Move $- 3$ to the left of $x^{2}$ .

$x^{3} - 3 \cdot x^{2} + 25 x + 25 \cdot - 3$

Step 4.3

Multiply $25$ by $- 3$ .

$x^{3} - 3 x^{2} + 25 x - 75$