13-6 Multiplying Binomials Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation Pre-Algebra

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 x 2 – 14x 13-6 Multiplying Binomials 336 cm 2 Pre-Algebra

Problem of the Day Find the missing term in the given arithmetic sequence , 155, ,,,, 140,... Pre-Algebra 13-6 Multiplying Binomials

Learn to multiply binomials. Pre-Algebra 13-6 Multiplying Binomials

Vocabulary FOIL Insert Lesson Title Here Pre-Algebra 13-6 Multiplying 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 Pre-Algebra 13-6 Multiplying Binomials

The product can be written as FOIL: The First terms, the Outer terms, the Inner terms, and the Last terms of the binomials. 2 FirstLast Inner Outer Pre-Algebra 13-6 Multiplying Binomials

Multiply. Additional Example 1A & 1B: 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 Pre-Algebra 13-6 Multiplying Binomials

Additional Example 1C & 1D: 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 Pre-Algebra Combine like terms Multiplying Binomials

When you multiply two binomials, you will always get four products. Then look for like terms to combine. Helpful Hint Pre-Algebra 13-6 Multiplying Binomials

Try This: Example 1A & 1B Insert Lesson Title Here Pre-Algebra 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 13-6 Multiplying Binomials

Try This: Example 1C & 1D Insert Lesson Title Here Pre-Algebra 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 Multiplying Binomials

Base: 8 + 2x Height: x Area of the photo and frame combined: A = (8 + 2x)(10 + 2x) = x + 20x + 4x 2 = x + 4x Multiplying Binomials 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 8 · 10 = 80 in 2, so the frame area is x + 4x 2 – 80 = 36x + 4x 2 in Multiplying Binomials

Try This: Example 2 Find the area of the border of a computer screen of width x centimeters around a 50 cm by 80 cm screen. Represent the area of the border in terms of x. Insert Lesson Title Here Base: x Height: x Area of the screen and border combined: A = (80 + 2x)(50 + 2x) = x + 100x + 4x 2 = x + 4x Multiplying Binomials

Try This: Example 2 Continued Insert Lesson Title Here The screen area is 80 · 50 = 4000 cm 2, so the frame area is x + 4x 2 – 4000 = 260x + 4x 2 cm Multiplying Binomials

Binomial products of the form (a + b) 2, (a – b) 2, and (a + b)(a – b) are often called special products Multiplying Binomials

Multiply. Additional Example 3A & 3B: Special Products of Binomials A. (x + 6) 2 (x + 6) 2 (x + 6)(x + 6) x 2 +6x + 6x + 36 x x + 36 B. (n – m) 2 (n – m) 2 (n – m) n 2 – nm – nm + m 2 n 2 – 2nm + m Multiplying Binomials

Additional Example 3C: Special Products of Binomials C. (x – 7)(x + 7) (x – 7)(x + 7) Multiply. x 2 + 7x – 7x – 49 x 2 – Multiplying Binomials

Try This: Example 3A & 3B Insert Lesson Title Here 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 Multiplying Binomials

Try This: Example 3C Insert Lesson Title Here C. (x – y)(x + y) (x – y)(x + y) Multiply. x 2 + xy – xy – y 2 x 2 – y Multiplying Binomials

Special Products of Binomials (a + b) 2 = a 2 + ab + ab + b 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – ab – ab + b 2 = a 2 – 2ab + b 2 (a + b)(a – b) = a 2 – ab + ab – b 2 = a 2 – b Multiplying Binomials

Lesson Quiz: Part 1 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 Insert Lesson Title Here 2y 2 – 4y – 6 6mn + 4m + 6n + 4 x 2 + 7x Multiplying Binomials

Lesson Quiz: Part 2 Multiply. 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 Insert Lesson Title Here 4w w 13-6 Multiplying Binomials Pre-Algebra 13-6 Multiplying Binomials