Question

factor completely.
160t² - 250

Explanation:

Step1: Factor out GCF

First, find the greatest common factor (GCF) of 160 and 250, which is 10.
$160t^2 - 250 = 10(16t^2 - 25)$

Step2: Recognize difference of squares

Notice $16t^2 - 25$ is a difference of squares: $a^2 - b^2 = (a-b)(a+b)$, where $a=4t$, $b=5$.
$16t^2 - 25 = (4t - 5)(4t + 5)$

Step3: Combine factors

Substitute back into the expression from Step1.
$10(4t - 5)(4t + 5)$

Answer:

$10(4t - 5)(4t + 5)$