7.4 Distribution and Conjugates Brett Solberg AHS ‘11-’12

Warm-up 1) Multiply 3 4 × 3 16 2) Simplify 128 2 3) Add 9𝑦+9 + 4 𝑥 3 +4 𝑥 2 What HW problems do you want to review?

Today’s Agenda Distributing Radicals Rationalizing the Denominator Conjugates Don’t forget about the green midyear review packet

Distribution Property a(b + c) = 8(2x + 1) = 5 2 + 3 =

Distribution Examples 2 5 3 +3 7 = 3 2 + 3 =

Distribution Property (a + b)(a - b) = (x + 4)(x – 4) = (8 −5 𝑥 ) 8+5 𝑥 =

Distribution Property (a + b)2 = (x + 3)2 = 2 5 −𝑦 2 =

Distribution Examples ( 𝑎 +2 3 ) 3 𝑏 −4 3 = 3 + 2 2 =

Rationalizing the Denominator We do not want radicals in the denominator Multiply by a radical to make the denominator an integer. 2 3

Rationalizing the Denominator 10 7 4𝑎 3𝑏 4 𝑥 5 3 𝑦 3

Rationalizing the Denominator 3 7 3 2 1 4 2𝑥 7 3 𝑥 5 2𝑦

Conjugate a + 𝑏 a - 𝑏 2 + 5 5 − 3

Using Conjugates 2 3+ 2 5 3 − 7

Using Conjugates 1 2 + 3 2 3 −3 3 3 −3

Homework 7.4 pg 308 3 – 51 multiples of 3