To fully factorize the given expression [tex]\(35m^2 + 28m\)[/tex], follow these steps:
1. Identify the greatest common factor (GCF) of the coefficients:
- The coefficients of the terms are 35 and 28. The greatest common factor of 35 and 28 is 7.
2. Factor out the greatest common factor:
- First, let's rewrite the expression by factoring out the GCF, which is 7.
- We divide each term by the GCF and rewrite the expression:
[tex]\[
35m^2 + 28m = 7 \left(\frac{35m^2}{7} + \frac{28m}{7}\right)
\][/tex]
- Simplify the terms within the parentheses:
[tex]\[
\frac{35m^2}{7} = 5m^2 \quad \text{and} \quad \frac{28m}{7} = 4m
\][/tex]
- So, the expression becomes:
[tex]\[
7(5m^2 + 4m)
\][/tex]
3. Combine the factors:
- The fully factored form of the given expression is:
[tex]\[
7(5m^2 + 4m)
\][/tex]
Therefore, the fully factored form of [tex]\(35m^2 + 28m\)[/tex] is [tex]\(\boxed{7(5m^2 + 4m)}\)[/tex].
