Completely factor the expression by grouping, if possible.
3yb−8+6y^2−8y
To factor the given expression by grouping, we initially group terms that can be paired in such a way that each pair has a common factor.
The given expression is:
3yb−8+6y^2−8y
First, rearrange terms to group like terms:
6y^2 + 3yb - 8y - 8
Now, let's group the terms that have common factors:
(6y^2 + 3yb) - (8y + 8)
Next, factor out the common factor from each group:
3y(2y + b) - 8(1y + 1)
Notice that each group now has different factors, so this expression cannot be completely factored by grouping in its current form because there are no common binomial factors.
However, we can look for other factorization methods. The expression 2y + b and 1y + 1 are not the same and we cannot further factor the expression in its current arrangement by grouping.
The final expression remains factored as:
3y(2y + b) - 8(y + 1)