Algebra Examples

$- 80 x^{3} y + 40 x^{2} y^{2} - 5 x y^{3}$

Step 1

Factor $- 5 x y$ out of $- 80 x^{3} y + 40 x^{2} y^{2} - 5 x y^{3}$ .

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Step 1.1

Factor $- 5 x y$ out of $- 80 x^{3} y$ .

$- 5 x y (16 x^{2}) + 40 x^{2} y^{2} - 5 x y^{3}$

Step 1.2

Factor $- 5 x y$ out of $40 x^{2} y^{2}$ .

$- 5 x y (16 x^{2}) - 5 x y (- 8 x y) - 5 x y^{3}$

Step 1.3

Factor $- 5 x y$ out of $- 5 x y^{3}$ .

$- 5 x y (16 x^{2}) - 5 x y (- 8 x y) - 5 x y (y^{2})$

Step 1.4

Factor $- 5 x y$ out of $- 5 x y (16 x^{2}) - 5 x y (- 8 x y)$ .

$- 5 x y (16 x^{2} - 8 x y) - 5 x y (y^{2})$

Step 1.5

Factor $- 5 x y$ out of $- 5 x y (16 x^{2} - 8 x y) - 5 x y (y^{2})$ .

$- 5 x y (16 x^{2} - 8 x y + y^{2})$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$- 5 x y ({(4 x)}^{2} - 8 x y + y^{2})$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x y = 2 \cdot (4 x) \cdot y$

Step 2.3

Rewrite the polynomial.

$- 5 x y ({(4 x)}^{2} - 2 \cdot (4 x) \cdot y + y^{2})$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 4 x$ and $b = y$ .

$- 5 x y {(4 x - y)}^{2}$