7.3 Special Products

What We Will Learn Use square of a binomial pattern Use sum and difference pattern

Ex. 1 Square of a Binomial 𝑎+𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎 2 +2𝑎𝑏+ 𝑏 2 𝑎+𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎 2 +2𝑎𝑏+ 𝑏 2 𝑎−𝑏 2 = 𝑎−𝑏 𝑎−𝑏 = 𝑎 2 −2𝑎𝑏+ 𝑏 2 If forget pattern, just use any method of multiplying learned before FOIL, distribute, or table Multiply: 3𝑥+4 2 = 3𝑥+4 3𝑥+4 a = 3x b = 4 9𝑥 2 +24𝑥+16

Ex. 1 Cont. 5𝑥−2 2 Your Practice 5𝑥−2 5𝑥−2 7𝑥−3 2 25𝑥 2 −20𝑥+4 5𝑥−2 2 5𝑥−2 5𝑥−2 a = 5x b = -2 25𝑥 2 −20𝑥+4 4𝑥+𝑦 2 4𝑥+𝑦 4𝑥+𝑦 a = 4x b = 1y 16𝑥 2 +8𝑥𝑦+ 𝑦 2 Just put the two letter together in the middle Your Practice 7𝑥−3 2 a = 7x b = -3 49𝑥 2 −42𝑥+9 6𝑥+3𝑦 2 a = 6x b = 3y 36𝑥 2 +36𝑥𝑦+ 9𝑦 2

Ex. 2 Sum and Difference Pattern 𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2 Multiply: 𝑡−5 𝑡+5 a = 1t b = 5 𝑡 2 −25 2𝑥+3 2𝑥−3 a = 2x b = 3 4𝑥 2 −9 2𝑥+3𝑦 2𝑥−3𝑦 a = 2x b = 3y 4𝑥 2 − 9𝑦 2 Your Practice 𝑥+3 𝑥−3 𝑥 2 −9 𝑥+3𝑦 𝑥−3𝑦 𝑥 2 − 9𝑦 2

Ex. 3 Mental Math 26×34 16×24 20−4 20+4 Use difference of squares Find number between both 30 Use difference of squares 30−4 30+4 a = 30 b = 4 30 2 − 4 2 900-16 884 16×24 20 20−4 20+4 a = 20 b = 4 20 2 − 4 2 400−16 384

Ex. 3 Cont. Your Practice 33×27 45 2 29 2 29×29 30−1 30−1 30−1 30−1 Use square of binomial pattern 𝑎 2 −2𝑎𝑏 + 𝑏 2 a = 30 b = -1 30 2 −2 30 −1 + −1 2 900+60+1 961 Your Practice 33×27 30+3 30−3 900 – 9 891 45 2 45×45 40+5 40+5 1600 + 400 + 25 2025