Math 9 Honours Section 4.1 Multiplying & Dividing Polynomials

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

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

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

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

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

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

Practice: Expand the binomials

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

Practice: Expand each of the following

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

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