# Multiply (2 square root of 3+ square root of 2)(3 square root of 2- square root of 3) (23+2)(32-3)
Expand (23+2)(32-3) using the FOIL Method.
Apply the distributive property.
23(32-3)+2(32-3)
Apply the distributive property.
23(32)+23(-3)+2(32-3)
Apply the distributive property.
23(32)+23(-3)+2(32)+2(-3)
23(32)+23(-3)+2(32)+2(-3)
Simplify and combine like terms.
Simplify each term.
Multiply 23(32).
Multiply 3 by 2.
632+23(-3)+2(32)+2(-3)
Combine using the product rule for radicals.
62⋅3+23(-3)+2(32)+2(-3)
Multiply 2 by 3.
66+23(-3)+2(32)+2(-3)
66+23(-3)+2(32)+2(-3)
Multiply 23(-3).
Multiply -1 by 2.
66-233+2(32)+2(-3)
Raise 3 to the power of 1.
66-2(313)+2(32)+2(-3)
Raise 3 to the power of 1.
66-2(3131)+2(32)+2(-3)
Use the power rule aman=am+n to combine exponents.
66-231+1+2(32)+2(-3)
Add 1 and 1.
66-232+2(32)+2(-3)
66-232+2(32)+2(-3)
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
66-2(312)2+2(32)+2(-3)
Apply the power rule and multiply exponents, (am)n=amn.
66-2⋅312⋅2+2(32)+2(-3)
Combine 12 and 2.
66-2⋅322+2(32)+2(-3)
Cancel the common factor of 2.
Cancel the common factor.
66-2⋅322+2(32)+2(-3)
Divide 1 by 1.
66-2⋅31+2(32)+2(-3)
66-2⋅31+2(32)+2(-3)
Evaluate the exponent.
66-2⋅3+2(32)+2(-3)
66-2⋅3+2(32)+2(-3)
Multiply -2 by 3.
66-6+2(32)+2(-3)
Multiply 2(32).
Raise 2 to the power of 1.
66-6+3(212)+2(-3)
Raise 2 to the power of 1.
66-6+3(2121)+2(-3)
Use the power rule aman=am+n to combine exponents.
66-6+321+1+2(-3)
Add 1 and 1.
66-6+322+2(-3)
66-6+322+2(-3)
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
66-6+3(212)2+2(-3)
Apply the power rule and multiply exponents, (am)n=amn.
66-6+3⋅212⋅2+2(-3)
Combine 12 and 2.
66-6+3⋅222+2(-3)
Cancel the common factor of 2.
Cancel the common factor.
66-6+3⋅222+2(-3)
Divide 1 by 1.
66-6+3⋅21+2(-3)
66-6+3⋅21+2(-3)
Evaluate the exponent.
66-6+3⋅2+2(-3)
66-6+3⋅2+2(-3)
Multiply 3 by 2.
66-6+6+2(-3)
Multiply 2(-3).
Combine using the product rule for radicals.
66-6+6-2⋅3
Multiply 2 by 3.
66-6+6-6
66-6+6-6
66-6+6-6
Subtract 6 from 66.
-6+6+56
Add -6 and 6.
0+56
Add 0 and 56.
56
56
The result can be shown in multiple forms.
Exact Form:
56
Decimal Form:
12.24744871…
Multiply (2 square root of 3+ square root of 2)(3 square root of 2- square root of 3)

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