Factor 25x^2-10x+1

$25 x^{2} - 10 x + 1$

Step 1

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

${(5 x)}^{2} - 10 x + 1$

Step 2

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

${(5 x)}^{2} - 10 x + 1^{2}$

Step 3

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

$10 x = 2 \cdot (5 x) \cdot 1$

Step 4

Rewrite the polynomial.

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

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 1$ .

${(5 x - 1)}^{2}$