Algebra Examples

$(- 4 \sqrt{2}, - \sqrt{12})$ , $(- \sqrt{32}, 2 \sqrt{3})$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.1

Factor $4$ out of $12$ .

$(- 4 \sqrt{2}, - \sqrt{4 (3)}) - (- \sqrt{32}, 2 \sqrt{3})$

Step 1.2

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

$(- 4 \sqrt{2}, - \sqrt{2^{2} \cdot 3}) - (- \sqrt{32}, 2 \sqrt{3})$

Step 2

Pull terms out from under the radical.

$(- 4 \sqrt{2}, - (2 \sqrt{3})) - (- \sqrt{32}, 2 \sqrt{3})$

Step 3

Multiply $2$ by $- 1$ .

$(- 4 \sqrt{2}, - 2 \sqrt{3}) - (- \sqrt{32}, 2 \sqrt{3})$

Step 4

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 4.1

Factor $16$ out of $32$ .

$(- 4 \sqrt{2}, - 2 \sqrt{3}) - (- \sqrt{16 (2)}, 2 \sqrt{3})$

Step 4.2

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

$(- 4 \sqrt{2}, - 2 \sqrt{3}) - (- \sqrt{4^{2} \cdot 2}, 2 \sqrt{3})$

Step 5

Pull terms out from under the radical.

$(- 4 \sqrt{2}, - 2 \sqrt{3}) - (- (4 \sqrt{2}), 2 \sqrt{3})$

Step 6

Multiply $4$ by $- 1$ .

$(- 4 \sqrt{2}, - 2 \sqrt{3}) - (- 4 \sqrt{2}, 2 \sqrt{3})$

Step 7

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 8

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{- 4 \sqrt{2} - 4 \sqrt{2}}{2}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 9

Subtract $4 \sqrt{2}$ from $- 4 \sqrt{2}$ .

$(\frac{- 8 \sqrt{2}}{2}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 10

Cancel the common factor of $- 8$ and $2$ .

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Step 10.1

Factor $2$ out of $- 8 \sqrt{2}$ .

$(\frac{2 (- 4 \sqrt{2})}{2}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $2$ .

$(\frac{2 (- 4 \sqrt{2})}{2 (1)}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 10.2.2

Cancel the common factor.

$(\frac{2 (- 4 \sqrt{2})}{2 \cdot 1}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 10.2.3

Rewrite the expression.

$(\frac{- 4 \sqrt{2}}{1}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 10.2.4

Divide $- 4 \sqrt{2}$ by $1$ .

$(- 4 \sqrt{2}, \frac{- 2 \sqrt{3} + 2 \sqrt{3}}{2})$

Step 11

Add $- 2 \sqrt{3}$ and $2 \sqrt{3}$ .

$(- 4 \sqrt{2}, \frac{0}{2})$

Step 12

Divide $0$ by $2$ .

$(- 4 \sqrt{2}, 0)$

Step 13