Algebra Examples

${(i - 5)}^{2} - 2 (i - 5) + 6$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(i - 5)}^{2}$ as $(i - 5) (i - 5)$ .

$(i - 5) (i - 5) - 2 (i - 5) + 6$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$i (i - 5) - 5 (i - 5) - 2 (i - 5) + 6$

Step 1.2.2

Apply the distributive property.

$i i + i \cdot - 5 - 5 (i - 5) - 2 (i - 5) + 6$

Step 1.2.3

Apply the distributive property.

$i i + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $i i$ .

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Step 1.3.1.1.1

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

$i^{1} i + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.1.2

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

$i^{1} i^{1} + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.1.3

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

$i^{1 + 1} + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.1.4

Add $1$ and $1$ .

$i^{2} + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.2

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

$- 1 + i \cdot - 5 - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.3

Move $- 5$ to the left of $i$ .

$- 1 - 5 \cdot i - 5 i - 5 \cdot - 5 - 2 (i - 5) + 6$

Step 1.3.1.4

Multiply $- 5$ by $- 5$ .

$- 1 - 5 i - 5 i + 25 - 2 (i - 5) + 6$

Step 1.3.2

Add $- 1$ and $25$ .

$24 - 5 i - 5 i - 2 (i - 5) + 6$

Step 1.3.3

Subtract $5 i$ from $- 5 i$ .

$24 - 10 i - 2 (i - 5) + 6$

Step 1.4

Apply the distributive property.

$24 - 10 i - 2 i - 2 \cdot - 5 + 6$

Step 1.5

Multiply $- 2$ by $- 5$ .

$24 - 10 i - 2 i + 10 + 6$

Step 2

Simplify by adding terms.

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Step 2.1

Add $24$ and $10$ .

$34 - 10 i - 2 i + 6$

Step 2.2

Add $34$ and $6$ .

$40 - 10 i - 2 i$

Step 2.3

Subtract $2 i$ from $- 10 i$ .

$40 - 12 i$