To simplify the given expression [tex]\(9m^2 + 72m\)[/tex]:
1. Identify the common factor in the terms:
- The coefficients 9 and 72 have a greatest common divisor (GCD) of 9.
- Both terms have a common factor of [tex]\(m\)[/tex].
2. Factor out the common factor:
- From each term, factor out [tex]\(9m\)[/tex].
3. Write each term in factored form:
- For the term [tex]\(9m^2\)[/tex]:
[tex]\(9m^2 = 9m \cdot m\)[/tex]
- For the term [tex]\(72m\)[/tex]:
[tex]\(72m = 9m \cdot 8\)[/tex]
4. Combine the factored terms:
- When we factor out [tex]\(9m\)[/tex] from both terms, we get:
[tex]\[
9m^2 + 72m = 9m(m) + 9m(8) = 9m(m + 8)
\][/tex]
So, the factored form of the expression [tex]\(9m^2 + 72m\)[/tex] is:
[tex]\[
9m(m + 8)
\][/tex]
This is the simplified and fully factored version of the given quadratic expression.
