How do you evaluate #(6+ \sqrt { 7} ) ( 4- \sqrt { 7} )#?

1 Answer
Douglas K.
Sep 18, 2017

You can use the F.O.I.L. method but that only applies to binomials (such as these). A more general method is to write each term of the first factor as a multiplier of the second factor.

Explanation:

Write each term of the first factor as a multiplier of the second factor:

#(6+ sqrt7) (4-sqrt 7) = 6(4-sqrt7) + sqrt7(4-sqrt7)#

Use the distributive property on both terms of the right side:

#(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-sqrt7sqrt7#

The last term becomes -7:

#(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-7#

Combine like terms:

#(6+ sqrt7) (4-sqrt 7) = 17-2sqrt7#

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