Sure! Let's factor the expression [tex]\(\left(4 m^3+6 m^2\right)+(2 m+3)\)[/tex] by grouping. Here is the step-by-step solution:
1. Identify the two groups in the expression:
The expression [tex]\((4 m^3+6 m^2)+(2 m+3)\)[/tex] is already organized into two groups.
2. Factor out the greatest common factor (GCF) from each group:
- For the first group [tex]\(4 m^3 + 6 m^2\)[/tex], the GCF is [tex]\(2 m^2\)[/tex]:
[tex]\[
4 m^3 + 6 m^2 = 2 m^2 (2 m + 3)
\][/tex]
- For the second group [tex]\(2 m + 3\)[/tex], there is no common factor other than 1, so it remains unchanged:
[tex]\[
2 m + 3 = 1 (2 m + 3)
\][/tex]
3. Rewrite the expression using the factored groups:
[tex]\[
(4 m^3 + 6 m^2) + (2 m + 3) = 2 m^2 (2 m + 3) + 1(2 m + 3)
\][/tex]
4. Factor out the common binomial factor [tex]\((2 m + 3)\)[/tex]:
[tex]\[
2 m^2 (2 m + 3) + 1 (2 m + 3) = (2 m^2 + 1)(2 m + 3)
\][/tex]
So, the factored form of the expression [tex]\(\left(4 m^3+6 m^2\right)+(2 m+3)\)[/tex] is:
[tex]\[
(2 m^2 + 1)(2 m + 3)
\][/tex]
