Multiplying Binomials Objectives To Multiply Two Binomials FOIL
Multiplying Binomials Objectives: • To Multiply Two Binomials FOIL • To multiply the sum and difference of two expressions • To square a binomial
Example 1 Multiply. (x + 2)(x + 3) FOIL i r s t u t s i d e i a n s s t i d e = (x)(x) + (x)(3) + (2)(x) + (2)(3) = x 2 + 3 x + 2 x + 6 = x 2 + 5 x + 6
Example 2 Multiply. (3 x + 2)(x + 5) = (3 x)(x) + (3 x)(5) + (2)(x) + (2)(5) = 3 x 2 + 15 x + 2 x + 10 = 3 x 2 + 17 x + 10
Example 3 Multiply. (4 ab + 3)(2 a 2 b + 1) = (4 ab)(2 a 2 b) + (4 ab)(1) +(3)(2 a 2 b) + (3)(1) = 8 a 3 b 2 + 4 ab + 6 a 2 b + 3
Practice 1 Multiply. 1) (x + 3)(x + 4) 2) (x + 3)(x – 5) 3) (2 x + 1)(x + 4)
Practice 2 Multiply. 4) (2 x 2 – 3)(x – 2) 5) (6 x 2 + 5)(2 x 3 + 1) 6) (2 xy + 4 x)(-2 y + y 2)
Multiplying Binomials – Special Products Objectives: • To multiply the sum and difference of two expressions • To square a binomial
Example 1 Multiply. (x + 6)(x – 6) = (x)(x) + (x)(-6) + (6)(x) + (6)(-6) = x 2 – 6 x + 6 x - 36 = x 2 - 36
Example 2 Multiply. (2 x + 4)(2 x – 4) = (2 x) + (2 x)(-4) + (4)(2 x) + (4)(-4) = 4 x 2 – 8 x + 8 x - 16 = 4 x 2 - 16
Example 3 Multiply. (-3 x + 4 y)(-3 x – 4 y) = (-3 x) + (-3 x)(-4 y) + (4 y)(-3 x) + (4 y)(-4 y) = 9 x 2 + 12 xy – 16 y 2 = 9 x 2 – 16 y 2
Practice Multiply. 1) (x + 2)(x – 2) 2) (x 2 + 7)(x 2 – 7) 3) (3 x + 5)(3 x – 5)
Example 4 Multiply. (x + 2)2 = (x + 2) = (x)(x) + (x)(2) + (2)(x) + (2)(2) = x 2 + 2 x + 4 = x 2 + 4 x + 4
Example 5 Multiply. (x - 3)2 = (x - 3) = (x)(x) + (x)(-3) + (-3)(x) + (-3) = x 2 - 3 x + 9 = x 2 - 6 x + 9
Example 6 Multiply. (2 x – 3 y)2 = (2 x – 3 y) = (2 x) + (2 x)(-3 y) + (-3 y)(2 x) + (-3 y) = 4 x 2 - 6 xy + 9 y 2 = 4 x 2 - 12 xy + 9 y 2
Practice Multiply. 1) (x + 3)2 2) (2 x + 1)2 3) (2 y + 4 x)2
- Slides: 15