The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1
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WORKSHEET 7.6: MULTIPLYING TWO BINOMIALS
CONTAINING RADICALS
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Follow the steps below to multiply two binomials containing radicals:


  1. Multiply the first terms.

  2. Multiply the outer terms.

  3. Multiply the inner terms.

  4. Multiply the last terms.

  5. Add or subtract and simplify if necessary.


First Last

Inner

Outer

(√ 3 + (−2)) (√ 6 + 5)

EXAMPLE
(


3 −2)(


6 +5)


3 ·


6 =


18


3 · 5 = 5


3

− 2 ·


6 =− 2


6

− 2 · 5 =− 10


18 + 5


3 − 2


6 − 10 =


9


2 + 5


3 − 2


6 − 10 = 3


2 + 5


3 − 2


6 − 10

DIRECTIONS: Simplify each expression.



  1. (



7 +3)(


3 +5) 2. (3+



11)(3−



  1. 3.(



3 +


2)(


3 +


2)


  1. (



5 −


3)(


8 +2) 5. (



8 −


5)(


6 −



  1. 6.(4−



2)(2−


5)

CHALLENGE:Joelle’s teacher told her that multiplying two binomials that
contain radicals does not necessarily mean the product will contain a
radical. Do you agree with this statement? Provide an example if you agree
or a counterexample if you disagree.

263

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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