What is (1−3√7)(4−3√7)?

1 Answer
Lucio Falabella
Mar 16, 2016

(1−3√7)(4−3√7)=67−15√7

Explanation:

You could think that

√7=a

Therefore

(1−3√7)(4−3√7)=(1−3a)(4−3a)

that becomes a polinomial product

(1−3a)(4−3a)=1⋅4−1⋅3a−3a⋅4+(3a)2=
=4−3a−12a+9a2=4−15a+9a2=

Now you substitute a with √7

=4−15√7+9⋅7=4+63−15√7=67−15√7

With practice you will be able to avoid the substitution and compute the product immediately.

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