Evaluate 1/((3-2 square root of 2)^3)+1/((3+2 square root of 2)^3)

Math
1(3-22)3+1(3+22)3
Simplify each term.
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Use the Binomial Theorem.
133+3⋅32(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Simplify each term.
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Raise 3 to the power of 3.
127+3⋅32(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Multiply 3 by 32 by adding the exponents.
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Multiply 3 by 32.
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Raise 3 to the power of 1.
127+31⋅32(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Use the power rule aman=am+n to combine exponents.
127+31+2(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
127+31+2(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Add 1 and 2.
127+33(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
127+33(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Raise 3 to the power of 3.
127+27(-22)+3⋅3(-22)2+(-22)3+1(3+22)3
Multiply -2 by 27.
127-542+3⋅3(-22)2+(-22)3+1(3+22)3
Multiply 3 by 3.
127-542+9(-22)2+(-22)3+1(3+22)3
Apply the product rule to -22.
127-542+9((-2)222)+(-22)3+1(3+22)3
Raise -2 to the power of 2.
127-542+9(422)+(-22)3+1(3+22)3
Rewrite 22 as 2.
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Use axn=axn to rewrite 2 as 212.
127-542+9(4(212)2)+(-22)3+1(3+22)3
Apply the power rule and multiply exponents, (am)n=amn.
127-542+9(4⋅212⋅2)+(-22)3+1(3+22)3
Combine 12 and 2.
127-542+9(4⋅222)+(-22)3+1(3+22)3
Cancel the common factor of 2.
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Cancel the common factor.
127-542+9(4⋅222)+(-22)3+1(3+22)3
Divide 1 by 1.
127-542+9(4⋅21)+(-22)3+1(3+22)3
127-542+9(4⋅21)+(-22)3+1(3+22)3
Evaluate the exponent.
127-542+9(4⋅2)+(-22)3+1(3+22)3
127-542+9(4⋅2)+(-22)3+1(3+22)3
Multiply 4 by 2.
127-542+9⋅8+(-22)3+1(3+22)3
Multiply 9 by 8.
127-542+72+(-22)3+1(3+22)3
Apply the product rule to -22.
127-542+72+(-2)323+1(3+22)3
Raise -2 to the power of 3.
127-542+72-823+1(3+22)3
Rewrite 23 as (23)12.
127-542+72-823+1(3+22)3
Raise 2 to the power of 3.
127-542+72-88+1(3+22)3
Rewrite 8 as 22⋅2.
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Factor 4 out of 8.
127-542+72-84(2)+1(3+22)3
Rewrite 4 as 22.
127-542+72-822⋅2+1(3+22)3
127-542+72-822⋅2+1(3+22)3
Pull terms out from under the radical.
127-542+72-8(22)+1(3+22)3
Multiply 2 by -8.
127-542+72-162+1(3+22)3
127-542+72-162+1(3+22)3
Add 27 and 72.
199-542-162+1(3+22)3
Subtract 162 from -542.
199-702+1(3+22)3
Multiply 199-702 by 99+70299+702.
199-702⋅99+70299+702+1(3+22)3
Multiply 199-702 and 99+70299+702.
99+702(99-702)(99+702)+1(3+22)3
Expand the denominator using the FOIL method.
99+7029801+69302-69302-490022+1(3+22)3
Simplify.
99+7021+1(3+22)3
Divide 99+702 by 1.
99+702+1(3+22)3
Use the Binomial Theorem.
99+702+133+3⋅32(22)+3⋅3(22)2+(22)3
Simplify each term.
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Raise 3 to the power of 3.
99+702+127+3⋅32(22)+3⋅3(22)2+(22)3
Multiply 3 by 32 by adding the exponents.
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Multiply 3 by 32.
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Raise 3 to the power of 1.
99+702+127+31⋅32(22)+3⋅3(22)2+(22)3
Use the power rule aman=am+n to combine exponents.
99+702+127+31+2(22)+3⋅3(22)2+(22)3
99+702+127+31+2(22)+3⋅3(22)2+(22)3
Add 1 and 2.
99+702+127+33(22)+3⋅3(22)2+(22)3
99+702+127+33(22)+3⋅3(22)2+(22)3
Raise 3 to the power of 3.
99+702+127+27(22)+3⋅3(22)2+(22)3
Multiply 2 by 27.
99+702+127+542+3⋅3(22)2+(22)3
Multiply 3 by 3.
99+702+127+542+9(22)2+(22)3
Apply the product rule to 22.
99+702+127+542+9(2222)+(22)3
Raise 2 to the power of 2.
99+702+127+542+9(422)+(22)3
Rewrite 22 as 2.
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Use axn=axn to rewrite 2 as 212.
99+702+127+542+9(4(212)2)+(22)3
Apply the power rule and multiply exponents, (am)n=amn.
99+702+127+542+9(4⋅212⋅2)+(22)3
Combine 12 and 2.
99+702+127+542+9(4⋅222)+(22)3
Cancel the common factor of 2.
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Cancel the common factor.
99+702+127+542+9(4⋅222)+(22)3
Divide 1 by 1.
99+702+127+542+9(4⋅21)+(22)3
99+702+127+542+9(4⋅21)+(22)3
Evaluate the exponent.
99+702+127+542+9(4⋅2)+(22)3
99+702+127+542+9(4⋅2)+(22)3
Multiply 4 by 2.
99+702+127+542+9⋅8+(22)3
Multiply 9 by 8.
99+702+127+542+72+(22)3
Apply the product rule to 22.
99+702+127+542+72+2323
Raise 2 to the power of 3.
99+702+127+542+72+823
Rewrite 23 as (23)12.
99+702+127+542+72+823
Raise 2 to the power of 3.
99+702+127+542+72+88
Rewrite 8 as 22⋅2.
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Factor 4 out of 8.
99+702+127+542+72+84(2)
Rewrite 4 as 22.
99+702+127+542+72+822⋅2
99+702+127+542+72+822⋅2
Pull terms out from under the radical.
99+702+127+542+72+8(22)
Multiply 2 by 8.
99+702+127+542+72+162
99+702+127+542+72+162
Add 27 and 72.
99+702+199+542+162
Add 542 and 162.
99+702+199+702
Multiply 199+702 by 99-70299-702.
99+702+199+702⋅99-70299-702
Multiply 199+702 and 99-70299-702.
99+702+99-702(99+702)(99-702)
Expand the denominator using the FOIL method.
99+702+99-7029801-69302+69302-490022
Simplify.
99+702+99-7021
Divide 99-702 by 1.
99+702+99-702
99+702+99-702
Simplify by adding terms.
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Add 99 and 99.
198+702-702
Subtract 702 from 702.
198+0
Add 198 and 0.
198
198
Evaluate 1/((3-2 square root of 2)^3)+1/((3+2 square root of 2)^3)

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