1. 7-5 Multiply a Polynomial by a Monomial
Algebra Glencoe McGraw-Hill Linda Stamper

2. You can use the distributive property to multiply a monomial by a polynomial.
The problem.
x(x2 + 2x + 4)
x(x2)
optional step +
x(2x) +
x(4)
Distribute. + +
Simplify.

3. Simplify.
Example 1
Example 2
3m(2m2 + 4m + 6)
4y(y2 3y + 5) –
Example 3
Example 4
2a2(2a3 3a2 + 3) –
3x2(8x2 5x + 2) –
Example 6
Example 5
Don’t forget to write your answer in standard form – alphabetical descending order.

4. Simplify.
Example 1
Example 2
3m(2m2 + 4m + 6)
4y(y2 3y + 5) –
3m(2m2) +
3m(4m) +
3m(6)
4y(y2 + -3y + 5) + +
4y(y2) +
4y(-3y) +
4y(5) + +
Undo double signs!

5. Simplify.
Example 4
Example 3
3x2(8x2 5x + 2) –
2a2(2a3 3a2 + 3) –
3x2(8x2 + -5x + 2)
2a2(2a3 + -3a2 + 3)
2a2(2a3) +
2a2(-3a2) +
2a2(3)
3x2(8x2) +
3x2(-5x) +
3x2(2) + + + +
Undo double signs!
Undo double signs!

6. Example 5
Example 6

7. Simplify.
The problem.
Change subtraction to addition.
Distribute.
Simplify.

8. Simplify.
Example 7
Example 8

9. Simplify.
Example 7

10. Simplify.
Example 8

11. Solve.
The problem.
Distribute.
Combine like terms.
Use inverse operations to solve.

12. Solve.
Example 9
Example 10
Example 11

13. Solve.
Example 9

14. Solve.
Example 10

15. Example 11

16. Homework
7-A6 Pages #16-21,26-31,36-39,44.