#### Answer

$s^{2}+2st-35t^{2}=(s+7t)(s-5t)$

#### Work Step by Step

$s^{2}+2st-35t^{2}$
To factor this trinomial, open two parentheses, both containing initially the square root of the first term.
Using the FOIL method backwards, find two values whose product is equal to the third term, $-35t^{2}$ and that the sum of their coefficients is equal to the coefficient of the second term, $2$:
These two values are $7t$ and $-5t$
$s^{2}+2st-35t^{2}=(s+7t)(s-5t)$