University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

277

Pages:

1
Author:

Amira Hester

Mini-Lecture 5.4 Special Products Learning Objectives: 1. Multiply two binomials using the FOIL Method. 2. Square a binomial. 3. Multiply the sum and difference of two terms. Examples: 1. Multiply using FOIL. a) (x + 7)(x – 12) b) (3x – 1)(2x + 5) c) (a – 2b)(a + 12b) 3 ⎞⎛ 1⎞ ⎛ d) ⎜ x + ⎟⎜ x − ⎟ 7 ⎠⎝ 6⎠ ⎝ c) (5x – 3y)2 d) (7a3 – 4)2 3 ⎞⎛ 3⎞ ⎛ c) ⎜ 2 x − ⎟⎜ 2 x + ⎟ 5 ⎠⎝ 5⎠ ⎝ d) (10x – 7y)(10x + 7y) 2. Multiply. (Square a binomial). a) (x + 4)2 b) (3x – 5)2 3. Multiply the sum and difference of two terms. a) (y – 3)(y + 3) b) (5x – 1)(5x + 1) 4. Mixed practice. Multiply using special products. a) (n + 13)2 e) ( −5a 2 b) (a – 4y)(a + 11y) )( + 10b −5a 2 − 7b) ) f) c) (t – 2)(t + 13) 4 ⎞⎛ 4⎞ ⎛ ⎜ 2 x − ⎟⎜ 2 x + ⎟ 7 ⎠⎝ 7⎠ ⎝ d) (3x + 5)(3x – 5) g) (4x + 13y)2 Teaching Notes: • • • • Many students find FOIL easy. In examples 2, some students will incorrectly “distribute” the exponent rather than squaring the binomial. For example: (x+4)2 = x2 + 42. Encourage students to recognize the special products rather than just “FOIL”-ing them. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. 11 1 x − ; 2a) x2+8x+16; 42 14 9 2b) 9x2-30x+25; 2c) 25x2-30xy+9y2; 2d) 49a6-56a3 +16; 3a) y2-9; 3b) 25x2-1; 3c) 4 x 2 − ; 25 Answers: 1a) x2- 5x –84; 1b) 6x2+13x-5; 1c) a2+10ab-24b2; 1d) x 2 + 3d) 100x2 – 49y2; 4a) n2+26n+169; 4b) a2+7ay-44y2; 4c) t2+11t-26; 4d) 9x2-25; 4e) 25a4-15a2b-70b2; 4f) 4 x 2 − 16 ; 4g) 16x2+104xy+169y2 49