Basic Math Examples

$(6 + \sqrt{- 49}) (3 - \sqrt{- 16})$

Step 1

Rewrite $- 49$ as $- 1 (49)$ .

$(6 + \sqrt{- 1 (49)}) (3 - \sqrt{- 16})$

Step 2

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$(6 + \sqrt{- 1} \cdot \sqrt{49}) (3 - \sqrt{- 16})$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$(6 + i \cdot \sqrt{49}) (3 - \sqrt{- 16})$

Step 4

Rewrite $- 16$ as $- 1 (16)$ .

$(6 + i \cdot \sqrt{49}) (3 - \sqrt{- 1 (16)})$

Step 5

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$(6 + i \cdot \sqrt{49}) (3 - (\sqrt{- 1} \cdot \sqrt{16}))$

Step 6

Rewrite $\sqrt{- 1}$ as $i$ .

$(6 + i \cdot \sqrt{49}) (3 - (i \cdot \sqrt{16}))$

Step 7

Simplify terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

Rewrite $49$ as $7^{2}$ .

$(6 + i \cdot \sqrt{7^{2}}) (3 - (i \cdot \sqrt{16}))$

Step 7.1.2

Pull terms out from under the radical, assuming positive real numbers.

$(6 + i \cdot 7) (3 - (i \cdot \sqrt{16}))$

Step 7.1.3

Move $7$ to the left of $i$ .

$(6 + 7 i) (3 - (i \cdot \sqrt{16}))$

Step 7.2

Simplify each term.

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Step 7.2.1

Rewrite $16$ as $4^{2}$ .

$(6 + 7 i) (3 - (i \cdot \sqrt{4^{2}}))$

Step 7.2.2

Pull terms out from under the radical, assuming positive real numbers.

$(6 + 7 i) (3 - (i \cdot 4))$

Step 7.2.3

Move $4$ to the left of $i$ .

$(6 + 7 i) (3 - (4 \cdot i))$

Step 7.2.4

Multiply $4$ by $- 1$ .

$(6 + 7 i) (3 - 4 i)$

Step 8

Expand $(6 + 7 i) (3 - 4 i)$ using the FOIL Method.

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Step 8.1

Apply the distributive property.

$6 (3 - 4 i) + 7 i (3 - 4 i)$

Step 8.2

Apply the distributive property.

$6 \cdot 3 + 6 (- 4 i) + 7 i (3 - 4 i)$

Step 8.3

Apply the distributive property.

$6 \cdot 3 + 6 (- 4 i) + 7 i \cdot 3 + 7 i (- 4 i)$

Step 9

Simplify and combine like terms.

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply $6$ by $3$ .

$18 + 6 (- 4 i) + 7 i \cdot 3 + 7 i (- 4 i)$

Step 9.1.2

Multiply $- 4$ by $6$ .

$18 - 24 i + 7 i \cdot 3 + 7 i (- 4 i)$

Step 9.1.3

Multiply $3$ by $7$ .

$18 - 24 i + 21 i + 7 i (- 4 i)$

Step 9.1.4

Multiply $7 i (- 4 i)$ .

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Step 9.1.4.1

Multiply $- 4$ by $7$ .

$18 - 24 i + 21 i - 28 i i$

Step 9.1.4.2

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

$18 - 24 i + 21 i - 28 (i^{1} i)$

Step 9.1.4.3

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

$18 - 24 i + 21 i - 28 (i^{1} i^{1})$

Step 9.1.4.4

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

$18 - 24 i + 21 i - 28 i^{1 + 1}$

Step 9.1.4.5

Add $1$ and $1$ .

$18 - 24 i + 21 i - 28 i^{2}$

Step 9.1.5

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

$18 - 24 i + 21 i - 28 \cdot - 1$

Step 9.1.6

Multiply $- 28$ by $- 1$ .

$18 - 24 i + 21 i + 28$

Step 9.2

Add $18$ and $28$ .

$46 - 24 i + 21 i$

Step 9.3

Add $- 24 i$ and $21 i$ .

$46 - 3 i$