Basic Math Examples

$\frac{24 t^{6} y^{9} - 45 t^{7} y^{8} + 6 t^{8} y^{7} - 24 t^{9} y^{6}}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1

Factor $3 t^{6} y^{6}$ out of $24 t^{6} y^{9} - 45 t^{7} y^{8} + 6 t^{8} y^{7} - 24 t^{9} y^{6}$ .

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Step 1.1

Factor $3 t^{6} y^{6}$ out of $24 t^{6} y^{9}$ .

$\frac{3 t^{6} y^{6} (8 y^{3}) - 45 t^{7} y^{8} + 6 t^{8} y^{7} - 24 t^{9} y^{6}}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.2

Factor $3 t^{6} y^{6}$ out of $- 45 t^{7} y^{8}$ .

$\frac{3 t^{6} y^{6} (8 y^{3}) + 3 t^{6} y^{6} (- 15 t y^{2}) + 6 t^{8} y^{7} - 24 t^{9} y^{6}}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.3

Factor $3 t^{6} y^{6}$ out of $6 t^{8} y^{7}$ .

$\frac{3 t^{6} y^{6} (8 y^{3}) + 3 t^{6} y^{6} (- 15 t y^{2}) + 3 t^{6} y^{6} (2 t^{2} y) - 24 t^{9} y^{6}}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.4

Factor $3 t^{6} y^{6}$ out of $- 24 t^{9} y^{6}$ .

$\frac{3 t^{6} y^{6} (8 y^{3}) + 3 t^{6} y^{6} (- 15 t y^{2}) + 3 t^{6} y^{6} (2 t^{2} y) + 3 t^{6} y^{6} (- 8 t^{3})}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.5

Factor $3 t^{6} y^{6}$ out of $3 t^{6} y^{6} (8 y^{3}) + 3 t^{6} y^{6} (- 15 t y^{2})$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2}) + 3 t^{6} y^{6} (2 t^{2} y) + 3 t^{6} y^{6} (- 8 t^{3})}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.6

Factor $3 t^{6} y^{6}$ out of $3 t^{6} y^{6} (8 y^{3} - 15 t y^{2}) + 3 t^{6} y^{6} (2 t^{2} y)$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y) + 3 t^{6} y^{6} (- 8 t^{3})}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 1.7

Factor $3 t^{6} y^{6}$ out of $3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y) + 3 t^{6} y^{6} (- 8 t^{3})$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{3 t^{3} y^{4} - 6 t^{4} y^{3}}$

Step 2

Factor $3 t^{3} y^{3}$ out of $3 t^{3} y^{4} - 6 t^{4} y^{3}$ .

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Step 2.1

Factor $3 t^{3} y^{3}$ out of $3 t^{3} y^{4}$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{3 t^{3} y^{3} (y) - 6 t^{4} y^{3}}$

Step 2.2

Factor $3 t^{3} y^{3}$ out of $- 6 t^{4} y^{3}$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{3 t^{3} y^{3} (y) + 3 t^{3} y^{3} (- 2 t)}$

Step 2.3

Factor $3 t^{3} y^{3}$ out of $3 t^{3} y^{3} (y) + 3 t^{3} y^{3} (- 2 t)$ .

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{3 t^{3} y^{3} (y - 2 t)}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{3 t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{3 t^{3} y^{3} (y - 2 t)}$

Step 3.2

Rewrite the expression.

$\frac{t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{t^{3} y^{3} (y - 2 t)}$

Step 4

Cancel the common factor of $t^{6}$ and $t^{3}$ .

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Step 4.1

Factor $t^{3}$ out of $t^{6} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})$ .

$\frac{t^{3} (t^{3} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3}))}{t^{3} y^{3} (y - 2 t)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $t^{3}$ out of $t^{3} y^{3} (y - 2 t)$ .

$\frac{t^{3} (t^{3} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3}))}{t^{3} (y^{3} (y - 2 t))}$

Step 4.2.2

Cancel the common factor.

$\frac{t^{3} (t^{3} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3}))}{t^{3} (y^{3} (y - 2 t))}$

Step 4.2.3

Rewrite the expression.

$\frac{t^{3} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{y^{3} (y - 2 t)}$

Step 5

Cancel the common factor of $y^{6}$ and $y^{3}$ .

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Step 5.1

Factor $y^{3}$ out of $t^{3} y^{6} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})$ .

$\frac{y^{3} (t^{3} y^{3} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3}))}{y^{3} (y - 2 t)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{y^{3} (t^{3} y^{3} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3}))}{y^{3} (y - 2 t)}$

Step 5.2.2

Rewrite the expression.

$\frac{t^{3} y^{3} (8 y^{3} - 15 t y^{2} + 2 t^{2} y - 8 t^{3})}{y - 2 t}$