Name Date
WORKSHEET 7.6: MULTIPLYING TWO BINOMIALS
CONTAINING RADICALS
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Follow the steps below to multiply two binomials containing radicals:
- Multiply the first terms.
- Multiply the outer terms.
- Multiply the inner terms.
- Multiply the last terms.
- 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.
- (
√
7 +3)(
√
3 +5) 2. (3+
√
11)(3−
√
- 3.(
√
3 +
√
2)(
√
3 +
√
2)
- (
√
5 −
√
3)(
√
8 +2) 5. (
√
8 −
√
5)(
√
6 −
√
- 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.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.