Basic Math Examples

$\frac{a^{2} - 8 y + 16}{y^{3} - 14 y^{2} + 40 y}$

Step 1

Factor $y$ out of $y^{3} - 14 y^{2} + 40 y$ .

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Step 1.1

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

$\frac{a^{2} - 8 y + 16}{y \cdot y^{2} - 14 y^{2} + 40 y}$

Step 1.2

Factor $y$ out of $- 14 y^{2}$ .

$\frac{a^{2} - 8 y + 16}{y \cdot y^{2} + y (- 14 y) + 40 y}$

Step 1.3

Factor $y$ out of $40 y$ .

$\frac{a^{2} - 8 y + 16}{y \cdot y^{2} + y (- 14 y) + y \cdot 40}$

Step 1.4

Factor $y$ out of $y \cdot y^{2} + y (- 14 y)$ .

$\frac{a^{2} - 8 y + 16}{y (y^{2} - 14 y) + y \cdot 40}$

Step 1.5

Factor $y$ out of $y (y^{2} - 14 y) + y \cdot 40$ .

$\frac{a^{2} - 8 y + 16}{y (y^{2} - 14 y + 40)}$

Step 2

Factor $y^{2} - 14 y + 40$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $40$ and whose sum is $- 14$ .

$- 10, - 4$

Step 2.2

Write the factored form using these integers.

$\frac{a^{2} - 8 y + 16}{y ((y - 10) (y - 4))}$

$\frac{a^{2} - 8 y + 16}{y (y - 10) (y - 4)}$