Multiply (2 square root of 5-3 square root of 3)(p+3 square root of 3)

Math
(25-33)(p+33)
Expand (25-33)(p+33) using the FOIL Method.
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Apply the distributive property.
25(p+33)-33(p+33)
Apply the distributive property.
25p+25(33)-33(p+33)
Apply the distributive property.
25p+25(33)-33p-33(33)
25p+25(33)-33p-33(33)
Simplify terms.
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Simplify each term.
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Multiply 25(33).
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Multiply 3 by 2.
25p+653-33p-33(33)
Combine using the product rule for radicals.
25p+63⋅5-33p-33(33)
Multiply 3 by 5.
25p+615-33p-33(33)
25p+615-33p-33(33)
Multiply -33(33).
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Multiply 3 by -3.
25p+615-33p-933
Raise 3 to the power of 1.
25p+615-33p-9(313)
Raise 3 to the power of 1.
25p+615-33p-9(3131)
Use the power rule aman=am+n to combine exponents.
25p+615-33p-931+1
Add 1 and 1.
25p+615-33p-932
25p+615-33p-932
Rewrite 32 as 3.
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Use axn=axn to rewrite 3 as 312.
25p+615-33p-9(312)2
Apply the power rule and multiply exponents, (am)n=amn.
25p+615-33p-9⋅312⋅2
Combine 12 and 2.
25p+615-33p-9⋅322
Cancel the common factor of 2.
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Cancel the common factor.
25p+615-33p-9⋅322
Divide 1 by 1.
25p+615-33p-9⋅31
25p+615-33p-9⋅31
Evaluate the exponent.
25p+615-33p-9⋅3
25p+615-33p-9⋅3
Multiply -9 by 3.
25p+615-33p-27
25p+615-33p-27
Move 615.
25p-33p+615-27
25p-33p+615-27
Multiply (2 square root of 5-3 square root of 3)(p+3 square root of 3)

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