Factor 25c^2-20c+4

$25 c^{2} - 20 c + 4$

Step 1

Rewrite $25 c^{2}$ as ${(5 c)}^{2}$ .

${(5 c)}^{2} - 20 c + 4$

Step 2

Rewrite $4$ as $2^{2}$ .

${(5 c)}^{2} - 20 c + 2^{2}$

Step 3

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

$20 c = 2 \cdot (5 c) \cdot 2$

Step 4

Rewrite the polynomial.

${(5 c)}^{2} - 2 \cdot (5 c) \cdot 2 + 2^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 c$ and $b = 2$ .

${(5 c - 2)}^{2}$