Question

factor by grouping. \\(8y^3 - 6y^2 + 20y - 15\\)

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms:
$$(8y^{3}-6y^{2})+(20y - 15)$$

Step2: Factor out the GCF from each group

For the first group \(8y^{3}-6y^{2}\), the greatest common factor (GCF) is \(2y^{2}\). Factoring it out gives:
\(2y^{2}(4y - 3)\)
For the second group \(20y-15\), the GCF is \(5\). Factoring it out gives:
\(5(4y - 3)\)
So now the expression becomes:
\(2y^{2}(4y - 3)+5(4y - 3)\)

Step3: Factor out the common binomial factor

Notice that both terms have a common binomial factor of \((4y - 3)\). Factor that out:
\((4y - 3)(2y^{2}+5)\)

Answer:

\((4y - 3)(2y^{2}+5)\)