Algebra Examples

(5 + 4 i^{2}) + (9 - 4 i^{4})

$(5 + 4 i^{2}) + (9 - 4 i^{4})$

Step 1

Remove parentheses.

5 + 4 i^{2} + 9 - 4 i^{4}

$5 + 4 i^{2} + 9 - 4 i^{4}$

Step 2

Simplify each term.

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Step 2.1

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

5 + 4 \cdot - 1 + 9 - 4 i^{4}

$5 + 4 \cdot - 1 + 9 - 4 i^{4}$

Step 2.2

Multiply

4

$4$ by

- 1

$- 1$ .

5 - 4 + 9 - 4 i^{4}

$5 - 4 + 9 - 4 i^{4}$

Step 2.3

Rewrite

i^{4}

$i^{4}$ as

1

$1$ .

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Step 2.3.1

Rewrite

i^{4}

$i^{4}$ as

{(i^{2})}^{2}

${(i^{2})}^{2}$ .

5 - 4 + 9 - 4 {(i^{2})}^{2}

$5 - 4 + 9 - 4 {(i^{2})}^{2}$

Step 2.3.2

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

5 - 4 + 9 - 4 {(- 1)}^{2}

$5 - 4 + 9 - 4 {(- 1)}^{2}$

Step 2.3.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

5 - 4 + 9 - 4 \cdot 1

$5 - 4 + 9 - 4 \cdot 1$

5 - 4 + 9 - 4 \cdot 1

$5 - 4 + 9 - 4 \cdot 1$

Step 2.4

Multiply

- 4

$- 4$ by

1

$1$ .

5 - 4 + 9 - 4

$5 - 4 + 9 - 4$

5 - 4 + 9 - 4

$5 - 4 + 9 - 4$

Step 3

Simplify by adding and subtracting.

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Step 3.1

Subtract

4

$4$ from

5

$5$ .

1 + 9 - 4

$1 + 9 - 4$

Step 3.2

Add

1

$1$ and

9

$9$ .

10 - 4

$10 - 4$

Step 3.3

Subtract

4

$4$ from

10

$10$ .

6

$6$

6

$6$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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