1. Operations with Radical Expressions
Chapter 10 Section 2

2. Add and Subtract Radical Expressions
Monomials
Radical Expressions
15y – 3y = (15 – 3)y
= 12y
2x + 7x = (2 + 7)x
= 9x =
= 9 11
−3 2 = 15−3 2
= 12 2

3. Add and Subtract Radical Expressions
−5 3
(4 + 6 – 5) 3
5 3
−8 5
(12-8) (3+6) 7
cannot be simplified further because the radicands are different and there are no common factors. Also, each radicand is in simplest form already. If the radicals in an expression are not in simplest form, simplify them first.

4. Add and Subtract Radical Expressions with unlike radicands
Simplify
= 2 2∙2∙5 = 2(2 5 ) = 4 5
= 3 3∙3∙5 = 3(3 5 ) = 9 5
180 = 6∙6∙5 = 6 5
(4+9+6) 5
19 5

5. Multiply Radical Expressions
FOIL- First terms, Outer terms, Inner terms, Last terms
Foil Review: Find the product of (2y +3)(6y-7)
F O I L
(2y)(6y) + (2y)(-7) + (3)(6y) + (3)(-7)
12 𝑦 y y (-21)
12 𝑦 2 + 4y - 21

6. Multiply Radical Expressions
(4 5 −2 3 )(3 6 − 10 )
F O I L
(4 5 )(3 6 )+(4 5 )(- 10 )+(-2 3 )(3 6 )+( )(- 10 )
∙5∙ ∙3∙

7. Multiply Radical Expressions
Try on your own:
(5 5 – 4 3 )( −2 6 )

8. Homework
Page 538 #1-23 odd, 31, 33, 42, 43