Answer
$6a^6(4a+5b)(2a-3b)$
Work Step by Step
Step 1. Factor out $6a^6$ to get $48a^8-12a^7b-90a^6b^2=6a^6(8a^2-2ab-15b^2)$
Step 2. Find factors of $8$ as $(2)(4)$, and find factors of $-15$ as $(-3)(5)$
Step 3. Find the sum of cross product of the factors as $(4)(-3)+(2)(5)=-2$
Step 4. We have $8a^2-2ab-15b^2=(4a+5b)(2a-3b)$
Step 5. Thus $48a^8-12a^7b-90a^6b^2=6a^6(8a^2-2ab-15b^2)=6a^6(4a+5b)(2a-3b)$
