What are the steps to Multiply: (√[6] + 2√[2])(4√[6] – 3√[2])?

Answer 1

The distributive property is the standard way to do it: a(b + c) = ab + ac.

Apply it once to get rid of the first parentheses:
(√[6] + 2√[2])(4√[6] – 3√[2]) =
√[6](4√[6] – 3√[2]) + 2√[2](4√[6] – 3√[2])

And then twice more, once on each of the resulting terms:
√[6](4√[6] – 3√[2]) =
√[6](4√[6] + (√[6])(–3√[2])

2√[2](4√[6] – 3√[2]) =
2√[2](4√[6]) + 2√[2](–3√[2])

Then add all that up.

As a shorthand, you can use FOIL when you are multiplying two expressions with two terms each. It stands for the sum of the products of the:
* [F]irst terms (√[6] * 4√[6]) of each sum
* [O]uter terms (√[6] * – 3√[2]) furthest apart
* [I]nner terms (2√[2] * 4√[6]) closest together
* [L]ast terms (2√[2] * – 3√[2]) of each sum

(a + b)(c + d) = ac + ad + bc + bd

In this case your answer is:
√[6](4√[6] + (√[6])(–3√[2]) + 2√[2](4√[6]) + 2√[2](–3√[2])

... which simplifies to:

4*6 - 6√3 + 16√3 - 6*2
24 - 12 + 16√3 - 6√3
12 + 10√3

Answer 2

(√[6] + 2√[2])(4√[6] – 3√[2])
=4√(6*6) -3√(6*2) +2*4*√(2*6) -2*3√(2*2)
=24 - 3√(4*3) +8√(4*3) -6*2
=24 - 6√3 +16√3 -12
= 12 +10√3

Answer 3

use foil

F 4 sqtr (36) O -3 sqrt(12) I 8 sqrt (12) -6 sqrt (4)

and simplify

24 - 6 sqrt (3) + 16 sqrt (3) -12

combine like terms

12 + 10 sqrt (3)

Answer 4

(sqrt[6]+2 sqrt(2(4sqrt[6])=3sqrt[2])
=sqrt[6]x4 sqrt[6]]-2sqrt{2]x3sqrt[2]}-sqrt[6]x3sqrt[2]+2sqrt[2]x4sqrt[6]
=24-12-6sqrt[3]+16xsqrt[3]
=12+10xsqrt[3].ANS.

Answer 5

your face. :-P