Factor 25x^2-40x+16

$25 x^{2} - 40 x + 16$

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

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

Rewrite $16$ as $4^{2}$ .

${(5 x)}^{2} - 40 x + 4^{2}$

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

$40 x = 2 \cdot (5 x) \cdot 4$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 4$ .

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