(3+13)(3-13)

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 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

Add 1 and 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

Add -39 and 39.

-10+0

Add -10 and 0.

-10

-10

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