Answer:
3b(2n-5)(5n-2)
Step-by-step explanation:
to solve 30n²b - 87nb +30b, we would need to factor out a common term among them
the entire expression has the number 3 in common, as they are all factors of 3. each term has the letter b included as well, so we can factor out 3b from the expression
3b(10n² - 29n + 10)
now we can factor the expression 10n² - 29n + 10. there are many ways we can factor this. i am choosing to factor by grouping, which means breaking down the expression into 4 terms and factoring each term.
to break this down, we can write -29n as a difference. the expression looks as follows:
3b(10n² - 4n - 25n + 10)
now we seperate the new expression into 2 groups with 10n² - 4n being their own group, and -25n + 10 being another
we will now factor 10n² - 4n. both have 2n in common, so we will factor that out:
2n(5n - 2)
next is -25n + 10, both have 5 in common, but we want the factorization of -25n + 10 to be equal to 5n - 2. to do this, we would factor out a -5 to get a -2 out of 10
-5(5n - 2)
the expression looks like the following:
3b(2n(5n-2) -5 (5n-2)) < we can drop a 5n - 2 since there are 2 of them and combine 2n - 5 as another factor of the expression. the fully simplified expression looks like the following:
3b(2n-5)(5n-2) is our answer
