1. Math 9 Honours Section 4.1 Multiplying & Dividing Polynomials

2. I) Review
When multiplying two variables with the same base, you “add” the exponents
When dividing two variables with the same base, you “subtract” the exponents

3. When multiplying a polynomial with a monomial, distribute each term inside the brackets with the monomial.
One polynomial is the length and the other is the width
The product is the area of the rectangle formed by the two sides

4. Practice: Simplify the following
Expand by distributing
Expand by distributing
Expand by distributing
Combine Liketerms

5. When dividing polynomials, divide each term in the quotient by the monomial in the divisor
The polynomial in the numerator is the area
The divisor is the length of the rectangle
The quotient is the width of the rectangle

6. Practice simplify Divide each term by the Divide each term by the
denominator
Divide each term by the
denominator
Divide each term by the denominator
Simplify by combining liketerms

7. II) Multiplying two Binomials
When multiplying two binomials, use each binomial to form the sides of a rectangle
Expand to find the area
Another method for multiplying two binomials is by using FOIL
First
Outside
Inside
Last

8. Practice: Expand the binomials

9. II) Expanding Binomials with Trinomials
Make each term the sides of a polynomial
Expand and combine Like-Terms
Ex: Expand and Simplify:
Width: 2x + 3 Length: 4x2 – 7x + 12
Combine Like-Terms

10. Practice: Expand each of the following

11. Ex: Find the Area of the shaded Region
Split the area into 2 separate Rectangles
Find the Dimensions of each Rectangle
Find the Area of each Rectangle and add them together

12. Practice: Find the Area of the shaded Region
Split the area into 2 separate Rectangles
Find the Dimensions of each Rectangle
Find the Area of each Rectangle and add them together