# Multiply ( square root of 3+ square root of 13)( square root of 3- square root of 13)

(3+13)(3-13)
Expand (3+13)(3-13) using the FOIL Method.
Apply the distributive property.
3(3-13)+13(3-13)
Apply the distributive property.
33+3(-13)+13(3-13)
Apply the distributive property.
33+3(-13)+133+13(-13)
33+3(-13)+133+13(-13)
Simplify and combine like terms.
Simplify each term.
Combine using the product rule for radicals.
3⋅3+3(-13)+133+13(-13)
Multiply 3 by 3.
9+3(-13)+133+13(-13)
Rewrite 9 as 32.
32+3(-13)+133+13(-13)
Pull terms out from under the radical, assuming positive real numbers.
3+3(-13)+133+13(-13)
Multiply 3(-13).
Combine using the product rule for radicals.
3-3⋅13+133+13(-13)
Multiply 3 by 13.
3-39+133+13(-13)
3-39+133+13(-13)
Combine using the product rule for radicals.
3-39+13⋅3+13(-13)
Multiply 13 by 3.
3-39+39+13(-13)
Multiply 13(-13).
Raise 13 to the power of 1.
3-39+39-(13113)
Raise 13 to the power of 1.
3-39+39-(131131)
Use the power rule aman=am+n to combine exponents.
3-39+39-131+1
3-39+39-132
3-39+39-132
Rewrite 132 as 13.
Use axn=axn to rewrite 13 as 1312.
3-39+39-(1312)2
Apply the power rule and multiply exponents, (am)n=amn.
3-39+39-1312⋅2
Combine 12 and 2.
3-39+39-1322
Cancel the common factor of 2.
Cancel the common factor.
3-39+39-1322
Divide 1 by 1.
3-39+39-131
3-39+39-131
Evaluate the exponent.
3-39+39-1⋅13
3-39+39-1⋅13
Multiply -1 by 13.
3-39+39-13
3-39+39-13
Subtract 13 from 3.
-10-39+39
-10+0
-10
-10
Multiply ( square root of 3+ square root of 13)( square root of 3- square root of 13)

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