Precalculus Examples

$25 s^{2} - 10 s t + t^{2}$

Step 1

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

${(5 s)}^{2} - 10 s t + t^{2}$

Step 2

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

$10 s t = 2 \cdot (5 s) \cdot t$

Step 3

Rewrite the polynomial.

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

Step 4

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

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