1. Holt CA Course 1 12-6Multiplying Binomials Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 12-6Multiplying Binomials Warm Up Multiply. 1. x(x + 2) 2. – 3(p – 4) 3. 2x(3x – 7) 4. Find the area of a rectangle with length 16 cm and width 21 cm. x 2 + 2x – 3p + 12 6x 2 – 14x 336 cm 2

3. Holt CA Course 1 12-6Multiplying Binomials Preview of Algebra 1 10.0 Students add, subtract, multiply, and divide monomials, and polynomials. Students solve multistep problems, including word problems, by using these techniques. California Standards

4. Holt CA Course 1 12-6Multiplying Binomials Vocabulary FOIL

5. Holt CA Course 1 12-6Multiplying Binomials You can use the Distributive Property to multiply two binomials. (x + y)(x + z) = x(x + z) + y(x + z) = x 2 + xz + xy + yz

6. Holt CA Course 1 12-6Multiplying Binomials 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. 2 FirstLast Inner Outer

7. Holt CA Course 1 12-6Multiplying Binomials Multiply. Additional Example 1: Multiplying Two Binomials A. (n – 2)(m – 8) B. (x + 3)(x + z) (n – 2)(m – 8)(x + 3)(x + z) mn – 8n – 2m + 16 x 2 + xz + 3x + 3z FOIL

8. Holt CA Course 1 12-6Multiplying Binomials Additional Example 1: Multiplying Two Binomials Multiply. C. (a + 3)(a + 5) D. (x – 4y)(x + 7y) (a + 3)(a + 5)(x – 4y)(x + 7y) a 2 + 5a + 3a + 15x 2 + 7xy – 4xy – 28y 2 FOIL a 2 + 8a + 15 x 2 + 3xy – 28y 2 Combine like terms.

9. Holt CA Course 1 12-6Multiplying Binomials When you multiply two binomials, you will always get four products. Then combine like terms. Helpful Hint

10. Holt CA Course 1 12-6Multiplying Binomials Check It Out! Example 1 Multiply. A. (r – 4)(s – 6) B. (y + 2)(y + r) (r – 4)(s – 6)(y + 2)(y + r) rs – 6r – 4s + 24 y 2 + ry + 2y + 2r FOIL

11. Holt CA Course 1 12-6Multiplying Binomials Check It Out! Example 1 Multiply. C. (a + 3)(a + 4) D. (x – 3y)(x + 8y) (a + 3)(a + 4)(x – 3y)(x + 8y) a 2 + 4a + 3a + 12x 2 + 8xy – 3xy – 24y 2 FOIL a 2 + 7a + 12 x 2 + 5xy – 24y 2 Combine like terms.

12. Holt CA Course 1 12-6Multiplying Binomials Area of the frame = Total Area – Area of Photo A = (8 + 2x)(10 + 2x) = 80 + 16x + 20x + 4x 2 = 36x + 4x 2 An 8 in. by 10 in. photo has a wooden frame that extends x in. beyond each side. Represent the area of the frame in terms of x. Additional Example 2 The photo area is 36x + 4x 2 in 2. Total AreaArea of Photo – (8)(10) – 80

13. Holt CA Course 1 12-6Multiplying Binomials Check It Out! Example 2 Find the area of the border around a computer monitor of width x centimeters around a 50 cm by 80 cm screen. Represent the area of the border in terms of x. Total Area A = (80 + 2x)(50 + 2x) = 4000 + 160x + 100x + 4x 2 = 260x + 4x 2 The border area is 260x + 4x 2 cm 2. Area of border = Total Area – Area of Screen Area of Screen – (50)(80) – 4000

14. Holt CA Course 1 12-6Multiplying Binomials Binomial products of the form (a + b) 2, (a – b) 2, and (a + b)(a – b) are often called special products.

15. Holt CA Course 1 12-6Multiplying Binomials Multiply. Additional Example 3: Special Products of Binomials A. (x + 6) 2 (x + 6) 2 (x + 6)(x + 6) x 2 + 6x + 6x + 36 x 2 + 12x + 36 B. (n – m) 2 (n – m) 2 (n – m) n 2 – nm – nm + m 2 n 2 – 2nm + m 2

16. Holt CA Course 1 12-6Multiplying Binomials Additional Example 3: Special Products of Binomials C. (x – 7)(x + 7) (x – 7)(x + 7) Multiply. x 2 + 7x – 7x – 49 x 2 – 49 7x – 7x = 0

17. Holt CA Course 1 12-6Multiplying Binomials Check It Out! Example 3 Multiply. A. (x + y) 2 (x + y) 2 (x + y)(x + y) x 2 + xy + xy + y 2 x 2 + 2xy + y 2 B. (r – 3) 2 (r – 3) 2 (r – 3) r 2 – 3r – 3r + 9 r 2 – 6r + 9

18. Holt CA Course 1 12-6Multiplying Binomials Check It Out! Example 3 C. (x – y)(x + y) (x – y)(x + y) Multiply. x 2 + xy – xy – y 2 x 2 – y 2 xy – xy = 0

19. Holt CA Course 1 12-6Multiplying Binomials

20. Holt CA Course 1 12-6Multiplying Binomials Lesson Quiz Multiply. 1. (x + 5)(x + 2) 2. (c – 4)(c – 2) 3. (2y + 2)(y – 3) 4. (2m + 2)(3n + 2) c 2 – 6c + 8 2y 2 – 4y – 6 6mn + 4m + 6n + 4 x 2 + 7x + 10 5. (a – 1) 2 6. (b + 3)(b – 3) 7. Find the area of a cement walkway of width w yd that is around a 20 yd by 30 yd pool. b 2 – 9 a 2 – 2a + 1 4w 2 + 100w yd 2