Evaluate ( square root of 87- square root of 67)( square root of 87+ square root of 67)

Math
(87-67)(87+67)
Expand (87-67)(87+67) using the FOIL Method.
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Apply the distributive property.
87(87+67)-67(87+67)
Apply the distributive property.
8787+8767-67(87+67)
Apply the distributive property.
8787+8767-6787-6767
8787+8767-6787-6767
Simplify and combine like terms.
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Simplify each term.
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Combine using the product rule for radicals.
87⋅87+8767-6787-6767
Multiply 87 by 87.
7569+8767-6787-6767
Rewrite 7569 as 872.
872+8767-6787-6767
Pull terms out from under the radical, assuming positive real numbers.
87+8767-6787-6767
Combine using the product rule for radicals.
87+87⋅67-6787-6767
Multiply 87 by 67.
87+5829-6787-6767
Multiply -6787.
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Combine using the product rule for radicals.
87+5829-87⋅67-6767
Multiply 87 by 67.
87+5829-5829-6767
87+5829-5829-6767
Multiply -6767.
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Raise 67 to the power of 1.
87+5829-5829-(67167)
Raise 67 to the power of 1.
87+5829-5829-(671671)
Use the power rule aman=am+n to combine exponents.
87+5829-5829-671+1
Add 1 and 1.
87+5829-5829-672
87+5829-5829-672
Rewrite 672 as 67.
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Use axn=axn to rewrite 67 as 6712.
87+5829-5829-(6712)2
Apply the power rule and multiply exponents, (am)n=amn.
87+5829-5829-6712⋅2
Combine 12 and 2.
87+5829-5829-6722
Cancel the common factor of 2.
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Cancel the common factor.
87+5829-5829-6722
Divide 1 by 1.
87+5829-5829-671
87+5829-5829-671
Evaluate the exponent.
87+5829-5829-1⋅67
87+5829-5829-1⋅67
Multiply -1 by 67.
87+5829-5829-67
87+5829-5829-67
Subtract 67 from 87.
20+5829-5829
Subtract 5829 from 5829.
20+0
Add 20 and 0.
20
20
Evaluate ( square root of 87- square root of 67)( square root of 87+ square root of 67)

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