Multiplying Binomials Section 8-3 Part 1 & 2

Goals Goal Rubric To multiply two binomials or a binomial by a trinomial. Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary None

Multiplying Polynomials 3 Methods for multiplying polynomials Using the Distributive Property Can be used to multiply any two polynomials Using a Table or The Box Method Using FOIL Can only be used to multiply two binomials

Method 1: Distributive Property To multiply a binomial by a binomial, you can apply the Distributive Property more than once: (x + 3)(x + 2) =

Example: Multiply Using Distributive Property (s + 4)(s – 2)

Your Turn: Multiply. (a + 3)(a – 4)

Your Turn: Multiply. (y + 8)(y – 4)

Method 2: Box Method Visual model for distributing in polynomial products, works with any polynomial. Box method 2 x 2 parts = 2 rows 2 columns

Example: Multiply Using Box Method (x – 3)(4x – 5)

Your Turn: Multiply (3x + 1)(x + 4)

Your Turn: Multiply (2x - 5)(4x + 3)

Method 3: FOIL F O I L (x + y)(x + z) = x + xz xy yz The product can be simplified using the FOIL method: multiply the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials. F O I L First Last (x + y)(x + z) = x 2 + xz xy yz Inner Outer

Example: Multiply Using FOIL (x + 3)(x + 2) “First Outer Inner Last”, shortcut for distributing, only works with binomial-binomial products. F 1. Multiply the First terms. (x + 3)(x + 2) x x = x2  O 2. Multiply the Outer terms. (x + 3)(x + 2) x 2 = 2x  I 3. Multiply the Inner terms. (x + 3)(x + 2) 3 x = 3x  L 4. Multiply the Last terms. (x + 3)(x + 2) 3 2 = 6  (x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6 F O I L

Example: FOIL

Your Turn: Multiply. A. (m – 2)(m – 8) B. (x + 3)(x + 4)

Your Turn: Multiply. (x – 3)(x – 1)

Your Turn: Multiply. (2a – b2)(a + 4b2)

To multiply polynomials with more than two terms, you can use the Distributive Property several times. Multiply (5x + 3) by (2x2 + 10x – 6):

Write the product of the monomials in each row and column: You can also use the Box Method to multiply polynomials with more than two terms. Multiply (5x + 3) by (2x2 + 10x – 6): 2x2 +10x –6 5x +3 Write the product of the monomials in each row and column: To find the product, add all of the terms inside the box by combining like terms and simplifying if necessary.

Example: Multiply. (x – 5)(x2 + 4x – 6)

Your Turn: Multiply. (3x + 1)(x3 + 4x2 – 7) x3 4x2 –7 3x +1 Write the product of the monomials in each row and column. x3 4x2 –7 3x +1 Add all terms inside the rectangle.

Your Turn: Multiply. (x + 3)(x2 – 4x + 6)

Your Turn:

Example: Application The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height. Write a polynomial that represents the area of the base of the prism. A = l  w A = l w 

Your Turn: Find the area of the base when the height is 5 ft. The width of a rectangular prism is 3 feet less than the height, and the length of the prism is 4 feet more than the height. Find the area of the base when the height is 5 ft. A = h2 + h – 12