Factor 25x^2-80x+64

$25 x^{2} - 80 x + 64$

Step 1

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

${(5 x)}^{2} - 80 x + 64$

Step 2

Rewrite $64$ as $8^{2}$ .

${(5 x)}^{2} - 80 x + 8^{2}$

Step 3

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

$80 x = 2 \cdot (5 x) \cdot 8$

Step 4

Rewrite the polynomial.

${(5 x)}^{2} - 2 \cdot (5 x) \cdot 8 + 8^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 8$ .

${(5 x - 8)}^{2}$