1. Multiplying Binomials Mrs. Book Liberty Hill Middle School Algebra I

2. Bellwork  Simplify. Write the answer in standard form.  (x 3 + 3x 2 + x) + (5x 2 + x + 1)  m(4m 2 – 6) + 3m 2 (m + 9)  3d 2 (d 3 – 6) – d 3 (2d 2 + 4)

3. Multiplying Binomials Distributive Property Method – Vertical – Horizontal FOIL Method Applying Multiplication of Binomials

4. Distributive Method Vertical Method (2x + 3)(x + 5) 2x + 3 (×) x + 5 10x + 15 2x 2 + 3x + 10x + 15 Multiply by 5 Multiply by x 2x 2 + 3x

5. Distributive Method Horizontal Method (2x + 3)(x + 5) 2x (x + 5) + 3 (x + 5) Rewrite as the sum of two products Distribute 2x 2 + 10x + 3x + 15 2x 2 + 13x + 15 Combine like terms

6. FOIL Method To multiply two binomials find the sum of the products of F the First terms, O the Outer terms, I the Inner terms, and L the Last terms. ( 2x + 3 )( x + 5 ) 2x 2 + 13x + 15 2x22x2 + 10x + 3x+ 3x + 15 Combine like terms

7. Find the Product (3c – 5)(c + 3)

8. Find the Product (12t – 5)(12t + 5)

9. Find the Product (8w + 4x)(5w – 6x)

10. Applying Multiplication of Polynomials

11. You are planning a rectangular garden. Its length is twice its width x. You want a walkway 2 ft wide around the garden. a. Write an expression for the area of the garden and walk b. Write an expression for the area of the walk only. c. You have enough gravel to cover 76 ft 2 and want to use it all on the walk. How big should you make the garden?

12. Applying Multiplication of Polynomials Find an expression to represent the area of the shaded region