How do you multiply #(2+ 3\sqrt { 5} ) ( 2- 3\sqrt { 5} )#?

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Answer 1 · 2017-07-31T02:17:45

Use the pattern #(a+b)(a-b) = a^2-b^2#

The expression #( 2+ 3sqrt5)( 2- 3sqrt5)# fits the pattern:

#(a+b)(a-b) = a^2-b^2#

Therefore, we can merely write the product as the difference of 2 squares:

#( 2+ 3sqrt5)( 2- 3sqrt5) = (2)^2 - (3sqrt5)^2#

Simplifying:

#( 2+ 3sqrt5)( 2- 3sqrt5) = 4 - 9(5)#

#( 2+ 3sqrt5)( 2- 3sqrt5) = -41#