Algebra Examples

${(2 + i)}^{2} - 6 (2 + i) + 9$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(2 + i)}^{2}$ as $(2 + i) (2 + i)$ .

$(2 + i) (2 + i) - 6 (2 + i) + 9$

Step 1.2

Expand $(2 + i) (2 + i)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 (2 + i) + i (2 + i) - 6 (2 + i) + 9$

Step 1.2.2

Apply the distributive property.

$2 \cdot 2 + 2 i + i (2 + i) - 6 (2 + i) + 9$

Step 1.2.3

Apply the distributive property.

$2 \cdot 2 + 2 i + i \cdot 2 + i i - 6 (2 + i) + 9$

$2 \cdot 2 + 2 i + i \cdot 2 + i i - 6 (2 + i) + 9$

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 $2$ by $2$ .

$4 + 2 i + i \cdot 2 + i i - 6 (2 + i) + 9$

Step 1.3.1.2

Move $2$ to the left of $i$ .

$4 + 2 i + 2 \cdot i + i i - 6 (2 + i) + 9$

Step 1.3.1.3

Multiply $i i$ .

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Step 1.3.1.3.1

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

$4 + 2 i + 2 i + i^{1} i - 6 (2 + i) + 9$

Step 1.3.1.3.2

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

$4 + 2 i + 2 i + i^{1} i^{1} - 6 (2 + i) + 9$

Step 1.3.1.3.3

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

$4 + 2 i + 2 i + i^{1 + 1} - 6 (2 + i) + 9$

Step 1.3.1.3.4

Add $1$ and $1$ .

$4 + 2 i + 2 i + i^{2} - 6 (2 + i) + 9$

$4 + 2 i + 2 i + i^{2} - 6 (2 + i) + 9$

Step 1.3.1.4

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

$4 + 2 i + 2 i - 1 - 6 (2 + i) + 9$

$4 + 2 i + 2 i - 1 - 6 (2 + i) + 9$

Step 1.3.2

Subtract $1$ from $4$ .

$3 + 2 i + 2 i - 6 (2 + i) + 9$

Step 1.3.3

Add $2 i$ and $2 i$ .

$3 + 4 i - 6 (2 + i) + 9$

$3 + 4 i - 6 (2 + i) + 9$

Step 1.4

Apply the distributive property.

$3 + 4 i - 6 \cdot 2 - 6 i + 9$

Step 1.5

Multiply $- 6$ by $2$ .

$3 + 4 i - 12 - 6 i + 9$

$3 + 4 i - 12 - 6 i + 9$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12$ from $3$ .

$- 9 + 4 i - 6 i + 9$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $- 9$ and $9$ .

$0 + 4 i - 6 i$

Step 2.2.2

Add $0$ and $4 i$ .

$4 i - 6 i$

$4 i - 6 i$

Step 2.3

Subtract $6 i$ from $4 i$ .

$- 2 i$

$- 2 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$