What is the answer to this problem with explanation?

#(3sqrt10+5)(4sqrt6-2)#

2 Answers
Jim G.
Jun 18, 2018

#24sqrt15-6sqrt10+20sqrt6-10#

Explanation:

#"using the "color(blue)"law of radicals"#

#•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)#

#"expand the factors using FOIL"#

#=(3sqrt10xx4sqrt6)+(-2xx3sqrt10)+(5xx4sqrt6)#
#color(white)(=)+(5xx-2)#

#=12sqrt60-6sqrt10+20sqrt6-10#

#sqrt10" and "sqrt6" are in simplest form"#

#sqrt60=sqrt(4xx15)=sqrt4xxsqrt15=2sqrt15#

#sqrt15" is in simplest form"#

#=(12xx2sqrt15)-6sqrt10+20sqrt6-10#

#=24sqrt15-6sqrt10+20sqrt6-10#

F. Javier B.
Jun 18, 2018

#48sqrt15-6sqrt10+20sqrt6-10#
See below

Explanation:

We have to operate in this expresion usin distributive law for real numbers. This property stablish

#(a+d)(b+c)=ab+ac+db+dc#

#(3sqrt10+5)(4sqrt6-2)=3sqrt10·4sqrt6-3sqrt10·2+5·4sqrt6-5·2=12sqrt10sqrt6-6sqrt10+20sqrt6-10#

But #sqrt10sqrt6=sqrt60=sqrt(5·2^2·3)=2sqrt15#

Then

#12sqrt10sqrt6-6sqrt10+20sqrt6-10=24sqrt15-6sqrt10+20sqrt6-10#

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