Study Guide
Multiplying a Polynomial by a Monomial

 

The examples below show how the distributive property can be used to multiply a polynomial by a monomial. Examples 2 and 3 show that many equations must be added, subtracted, or multiplied before reaching the final solution.

 

Directions: Find each product.

10a + 15b

12x2 − 6xy

−4a2 + 4b2

8b4 − 4b2

−⅕ t4 + ⅕ t3 − t2

¼ xy + ½ y2

Directions: Solve each equation.

9. 3(x + 5) −6 = 18

 

 

3

10. 3x(x − 5) − 3x2 = −30

 

 

2

11. (4y − 3) − 8y + 6 = 19

 

 

−4

12. Ria's corn field has a perimeter of 18,000 meters. The length of one side is 3 meters less than twice the width. What are the dimensions of the field?

 

 

5999 meters by 3001 meters

  

13. Three sides of a triangle have measures that are consecutive even integers. What are the lengths of the sides if the perimeter is 114 meters?

 

 

36 meters, 38 meters, 40 meters