SOLUTION: Multiply: (8√[6] + 3√[2])(4√[6] – 5√[2]) I believe FOIL is used here. I also think the answer should have no decimals. Thanks for helping!!!

Algebra ->  Radicals -> SOLUTION: Multiply: (8√[6] + 3√[2])(4√[6] – 5√[2]) I believe FOIL is used here. I also think the answer should have no decimals. Thanks for helping!!!      Log On


   



Question 107625: Multiply:
(8√[6] + 3√[2])(4√[6] – 5√[2])
I believe FOIL is used here. I also think the answer should have no decimals.
Thanks for helping!!!

Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Yes FOIL Method (First Outer Inner Last)
(8√[6] + 3√[2])(4√[6] + (-5√[2])) Original Equation
First (8√[6]*4√[6])=32√[36]
First (8√[6]*4√[6])=32*6
First (8√[6]*4√[6])=192
Outer (8√[6]*-5√[2])=-40√[12]
Outer (8√[6]*-5√[2])=-80√[3]
Inner (3√[2]*4√[6])=12√[12]
Inner (3√[2]*4√[6])=24√[3]
Last (3√[2]*-5√[2])=-15√[4]
Last (3√[2]*-5√[2])=-15*2
Last (3√[2]*-5√[2])=-30
(8√[6]+3√[2])(4√[6]+(-5√[2]))=192+(-80√[3])+24√[3]+(-30) Combine all of the terms
(8√[6]+3√[2])(4√[6]+(-5√[2]))=162-56√[3] Final answer.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%288sqrt%286%29+%2B+3sqrt%282%29%29%284sqrt%286%29+-+5sqrt%282%29%29
The FOIL technique:
F stands for first terms,
O stands for outer terms,
I stands for inner terms, and
L stands for last terms.

F is the product of the first terms: %288sqrt%286%29%29%284sqrt%286%29%29+=+32%2A6+=+192
O+is the product of the outer terms: %283sqrt%282%29%29%28-5sqrt%282%29%29+=+-15%2A2+=+-30
I is the product of the inner two terms: %283sqrt%282%29%29%284sqrt%286%29%29+=+12sqrt%282%29%2Asqrt%286%29+
L is the product of the last two terms: %288sqrt%286%29%29%28-5sqrt%282%29%29+=+-+40sqrt%286%29sqrt%282%29

then we have:
%288sqrt%286%29+%2B+3sqrt%282%29%29%284sqrt%286%29+-+5sqrt%282%29%29
= 19230 + 12sqrt%282%29sqrt%286%2940+sqrt%286%29sqrt%282%29
= 162+%2B+%28sqrt%286%29sqrt%282%29%29%2812-40+%29
= 16228+%28sqrt%286%29sqrt%282%29%29
= 16228%282.45%29%281.41%29

= 162+-+96.726
= 65.274