Final answer:
The student's algebraic expression 7m2+(2m-1)(m+9) is expanded and simplified to 9m2+17m-9 by using distributive property to multiply and then combine like terms.
Step-by-step explanation:
The expression provided by the student, 7m2+(2m-1)(m+9), involves operations in algebra that requires expanding and simplifying a polynomial. To expand the expression, we use the distributive property to multiply each term in the second binomial (2m-1) by each term in the first binomial (m+9). Applying this method:
- Multiply 2m by m to get 2m2.
- Multiply 2m by 9 to get 18m.
- Multiply -1 by m to get -m.
- Multiply -1 by 9 to get -9.
After multiplication, we combine like terms:
- Combine 7m2 with 2m2 to get 9m2.
- Combine 18m with -m to get 17m.
The final expanded form of the expression is 9m2 + 17m - 9.
This type of problem helps students understand how to manipulate algebraic expressions, an essential skill for more complex math problems.