How do you simplify #(sqrt2 - 3 sqrt5) (sqrt2 + sqrt7)#?

1 Answer
Feb 7, 2016

Use the FOIL method of multiplying Binomials:

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#(sqrt2-3sqrt5)(sqrt2+sqrt7)#

#ul First#

#rarrsqrt2*sqrt2=2#

#ul Outer#

#rarrsqrt2*sqrt7=sqrt14#

#ul In##n##e##r#

#rarr-3sqrt5*sqrt2=-3sqrt10#

#ul La##st#

#rarr-3sqrt5*sqrt7=-3sqrt35#

Now combine them:

#(sqrt2-3sqrt5)(sqrt2+sqrt7)=2+sqrt14-3sqrt10-3sqrt35#