10b^-3-16b^25b-40

Question

cant seem to figure it out .

Answer 1

The expression you're asking about is unclear, you may have typed it incorrectly. The first term has a negative exponent which is possible but you may want to check that. What is most unclear is that there is no operation (+/-) separating the second term from the third term, and there is a caret symbol after what I'm assuming is the the second term (16b) which represents exponentiation but it's not clear whether the exponent is 2 or if the 2 that follows the symbol is actually part of what seems to be the third term, so the third term is either 5b or 25b. Lastly, what is it that they are asking you to do or solve for in this expression (e.g., factoring and, if so, is it by grouping?).

If I had to guess I would say you are trying to factor a 4 term polynomial expression by grouping, assuming that the expression looks like the following:

     10b³ - 16b² + 25b - 40

If this is the case and you are looking to factor by grouping, then take the following steps to do so:

(1)   group the first two terms and the last two terms separately

          10b³ - 16b²   +   25b - 40

(2)   find a gcf (greatest common factor) to factor out among each group

       10b³ - 16b²    ==> gcf:   2b²    ==>   2b²•5b  -  2b²•8  =  2b²•(5b - 8)

         25b - 40        ==> gcf:   5         ==>    5•5b  -  5•8  =  5•(5b - 8)

(3) substitute the factored form of each group into the original expression

          (10b³ - 16b²)  +  (25b - 40)

          (2b²•(5b - 8))  +  (5•(5b - 8))

(4) notice that the expression now has 2 terms (one from each group) and that these two terms share a common factor, that being  ' 5b - 8 ', which we can factor out from both terms

          2b²•(5b - 8)   +   5•(5b - 8)  =  (5b - 8)•2b²   +   (5b - 8)•5  

                                                    =  (5b - 8)•(2b² + 5)

Thus, factoring the original expression by grouping yields the following factored form of the expression:

          10b³ - 16b² + 25b - 40  =  (2b² + 5)(5b - 8)