Factor 25t^2-30t+9

$25 t^{2} - 30 t + 9$

Step 1

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

${(5 t)}^{2} - 30 t + 9$

Step 2

Rewrite $9$ as $3^{2}$ .

${(5 t)}^{2} - 30 t + 3^{2}$

Step 3

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

$30 t = 2 \cdot (5 t) \cdot 3$

Step 4

Rewrite the polynomial.

${(5 t)}^{2} - 2 \cdot (5 t) \cdot 3 + 3^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 t$ and $b = 3$ .

${(5 t - 3)}^{2}$