Teaching Notes 7.6: Multiplying Two Binomials
Containing Radicals
To multiply two binomials containing radicals, students must be familiar with multiplying radicals
and multiplying binomials. Common mistakes include using FOIL incorrectly, multiplying radicals
incorrectly, or simplifying radicals incorrectly.- Review how to multiply radicals with your students. Note that students must multiply
the radicands and simplify the radical. It may be helpful to look back at 7.2: ‘‘Multiplying
Radicals.’’ - Review the information and example on the worksheet with your students. Emphasize how
the FOIL method is used to multiply these terms. Depending on the abilities of your stu-
dents, it may be necessary to review multiplying binomials by presenting examples such as
(x+3)(x−2)=x^2 − 2 x+ 3 x− 6 =x^2 +x−6. Caution your students to pay close atten-
tion to negative signs. Remind them thatonly radicals with like radicands can be added or
subtracted.
EXTRA HELP:
You may simplify radicals before you multiply. However, it may still be necessary to check that all
radicals in the product are in simplest form.ANSWER KEY:
(1)√
21 + 5
√
7 + 3
√
3 + 15 (2)− 2 (3) 5 + 2
√
6 (4) 2
√
10 + 2
√
5 − 2
√
6 − 2
√
3
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(5) 4
√
3 − 2
√
6 −
√
30 +
√
15 (6) 8 − 4
√
5 − 2
√
2 +
√
10
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(Challenge)Joelle’s teacher is correct. (√
2 −
√
3)(
√
2 +
√
3)=−1.
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262 THE ALGEBRA TEACHER’S GUIDE