Factor 40xy^4-40xy^2z+10xz^2

$40 x y^{4} - 40 x y^{2} z + 10 x z^{2}$

Step 1

Factor $10 x$ out of $40 x y^{4} - 40 x y^{2} z + 10 x z^{2}$ .

Factor $10 x$ out of $40 x y^{4}$ .

$10 x (4 y^{4}) - 40 x y^{2} z + 10 x z^{2}$

Factor $10 x$ out of $- 40 x y^{2} z$ .

$10 x (4 y^{4}) + 10 x (- 4 y^{2} z) + 10 x z^{2}$

Factor $10 x$ out of $10 x z^{2}$ .

$10 x (4 y^{4}) + 10 x (- 4 y^{2} z) + 10 x (z^{2})$

Factor $10 x$ out of $10 x (4 y^{4}) + 10 x (- 4 y^{2} z)$ .

$10 x (4 y^{4} - 4 y^{2} z) + 10 x (z^{2})$

Factor $10 x$ out of $10 x (4 y^{4} - 4 y^{2} z) + 10 x (z^{2})$ .

$10 x (4 y^{4} - 4 y^{2} z + z^{2})$

Step 2

Factor using the perfect square rule.

Rewrite $4 y^{4}$ as ${(2 y^{2})}^{2}$ .

$10 x ({(2 y^{2})}^{2} - 4 y^{2} z + z^{2})$

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

$4 y^{2} z = 2 \cdot (2 y^{2}) \cdot z$

Rewrite the polynomial.

$10 x ({(2 y^{2})}^{2} - 2 \cdot (2 y^{2}) \cdot z + z^{2})$

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

$10 x {(2 y^{2} - z)}^{2}$