Section 7.3 Multiply a Monomial by a Polynomial We will be learning how to multiply a monomial (one term) by a polynomial (more than one term.

** Distributive Property** Is a rule for expanding an expression within brackets ( ) by multiplying each term inside the brackets by the term outside. Example: 4(7+6) = 4(7)+4(6) This Allows you to simplify expressions involving the multiplication of a monomial by a polynomial. Example: a(x+y)= ax+ay

METHOD 1: Area Model Example: 3(x+4) This means that you need to construct a rectangle with a width of 3 and length of x+4. You can see that the area of this rectangle is 3x+12 So therefore 3(x+4)= 3x+12 Multiply a Monomial by a Polynomial X+4 3

Method 2: Apply the Distributive Property Multiply each term inside the brackets by the term outside of the brackets Example: 3(x+4) = 3(x) +3(4) = 3x+12 Multiply a Monomial by a Polynomial

Expand and Simplify Expressions METHOD 1: Area Model Example: 4(x+1) + 2(x+2) Use tiles to create a rectangle for 4(x+1) and another for 2(x+2). Then collect like terms (types of tiles) 4(x+1) + 2(x+2) = 6x+8

Expand and Simplify Expressions METHOD 2: Apply the Distributive Property Example: 4(x+3)+2(2x-1) Apply the distributive property first to remove the brackets and then collect like terms 4(x+3)+2(2x-1) =4(x) + 4(3) + 2(2x) + 2(-1) =4x x -2 (COMBINE like terms) =8x +10

Expand and Simplify Expressions METHOD 3: Add the opposite polynomial This is used when subtracting polynomials Example: 3x(x+5) - (2x+1) First use distributive property, then to subtract (2x+1) add the opposite. 3x(x+5) - (2x+1) =3x(x)+3x(5)- (2x+1) = 3x x + (-2x-1) = 3x x -2x – 1 (COMBINE like terms) = 3x x – 1