Algebra Examples

$\frac{(6 u^{11} v^{6}) (11 u^{5} v)}{- 44 u^{11} v^{12}}$

Step 1

Expand $(6 u^{11} v^{6}) (11 u^{5} v)$ .

Tap for more steps...

Step 1.1

Remove parentheses.

$\frac{6 u^{11} v^{6} (11 u^{5}) v}{- 44 u^{11} v^{12}}$

Step 1.2

Remove parentheses.

$\frac{6 u^{11} v^{6} \cdot (11 u^{5} v)}{- 44 u^{11} v^{12}}$

Step 1.3

Move $v^{6}$ .

$\frac{6 u^{11} \cdot (11 v^{6} u^{5} v)}{- 44 u^{11} v^{12}}$

Step 1.4

Move $u^{11}$ .

$\frac{6 \cdot (11 u^{11} v^{6} u^{5} v)}{- 44 u^{11} v^{12}}$

Step 1.5

Multiply $6$ by $11$ .

$\frac{66 u^{11} v^{6} u^{5} v}{- 44 u^{11} v^{12}}$

Step 2

Turn the numerator into a polynomial.

Tap for more steps...

Step 2.1

Start expanding.

$(6 u^{11} v^{6}) (11 u^{5} v)$

Step 2.2

Remove parentheses.

$6 u^{11} v^{6} (11 u^{5}) v$

Step 2.3

Remove parentheses.

$6 u^{11} v^{6} \cdot 11 u^{5} v$

Step 2.4

Move $v^{6}$ .

$6 u^{11} \cdot 11 v^{6} u^{5} v$

Step 2.5

Move $u^{11}$ .

$6 \cdot 11 u^{11} v^{6} u^{5} v$

Step 2.6

Multiply $6$ by $11$ .

$66 u^{11} v^{6} u^{5} v$

Step 2.7

Multiply $u^{11}$ by $u^{5}$ by adding the exponents.

Tap for more steps...

Step 2.7.1

Move $u^{5}$ .

$66 (u^{5} u^{11}) v^{6} v$

Step 2.7.2

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

$66 u^{5 + 11} v^{6} v$

Step 2.7.3

Add $5$ and $11$ .

$66 u^{16} v^{6} v$

Step 2.8

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

$66 u^{16} (v^{1} v^{6})$

Step 2.9

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

$66 u^{16} v^{1 + 6}$

Step 2.10

Add $1$ and $6$ .

$66 u^{16} v^{7}$

Step 3

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

Step 4

Divide the highest order term in the dividend $66 u^{16} v^{7}$ by the highest order term in divisor $- 44 v^{12} u^{11}$ .

$\frac{3 u^{5}}{2 v^{5}}$

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

Step 5

Multiply the new quotient term by the divisor.

$\frac{3 u^{5}}{2 v^{5}}$

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $66 u^{16} v^{7} + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0$

$\frac{3 u^{5}}{2 v^{5}}$

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0$

Step 7

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$\frac{3 u^{5}}{2 v^{5}}$

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0$

Step 8

Pull the next terms from the original dividend down into the current dividend.

$\frac{3 u^{5}}{2 v^{5}}$

$44 v^{12} u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0 u^{15}$

$0 u^{14}$

$0 u^{13}$

$0 u^{12}$

$0 u^{11}$

$0 u^{10}$

$0 u^{9}$

$0 u^{8}$

$0 u^{7}$

$0 u^{6}$

$0 u^{5}$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

$66 u^{16} v^{7}$

$0$

$0 u^{4}$

$0 u^{3}$

$0 u^{2}$

$0 u$

$0$

Step 9

Since the remander is $0$ , the final answer is the quotient.

$- \frac{3 u^{5}}{2 v^{5}}$