Factor 20r^4s-20r^3s+5r^2s

$20 r^{4} s - 20 r^{3} s + 5 r^{2} s$

Factor $5 r^{2} s$ out of $20 r^{4} s - 20 r^{3} s + 5 r^{2} s$ .

Factor $5 r^{2} s$ out of $20 r^{4} s$ .

$5 r^{2} s (4 r^{2}) - 20 r^{3} s + 5 r^{2} s$

Factor $5 r^{2} s$ out of $- 20 r^{3} s$ .

$5 r^{2} s (4 r^{2}) + 5 r^{2} s (- 4 r) + 5 r^{2} s$

Factor $5 r^{2} s$ out of $5 r^{2} s$ .

$5 r^{2} s (4 r^{2}) + 5 r^{2} s (- 4 r) + 5 r^{2} s (1)$

Factor $5 r^{2} s$ out of $5 r^{2} s (4 r^{2}) + 5 r^{2} s (- 4 r)$ .

$5 r^{2} s (4 r^{2} - 4 r) + 5 r^{2} s (1)$

Factor $5 r^{2} s$ out of $5 r^{2} s (4 r^{2} - 4 r) + 5 r^{2} s (1)$ .

$5 r^{2} s (4 r^{2} - 4 r + 1)$

Factor using the perfect square rule.

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

$5 r^{2} s ({(2 r)}^{2} - 4 r + 1)$

Rewrite $1$ as $1^{2}$ .

$5 r^{2} s ({(2 r)}^{2} - 4 r + 1^{2})$

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

$4 r = 2 \cdot (2 r) \cdot 1$

Rewrite the polynomial.

$5 r^{2} s ({(2 r)}^{2} - 2 \cdot (2 r) \cdot 1 + 1^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 r$ and $b = 1$ .

$5 r^{2} s {(2 r - 1)}^{2}$