Simplify (3a-1)^3

Math
(3a-1)3
Use the Binomial Theorem.
(3a)3+3(3a)2⋅-1+3(3a)(-1)2+(-1)3
Simplify each term.
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Apply the product rule to 3a.
33a3+3(3a)2⋅-1+3(3a)(-1)2+(-1)3
Raise 3 to the power of 3.
27a3+3(3a)2⋅-1+3(3a)(-1)2+(-1)3
Apply the product rule to 3a.
27a3+3(32a2)⋅-1+3(3a)(-1)2+(-1)3
Multiply 3 by 32 by adding the exponents.
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Move 32.
27a3+32⋅3a2⋅-1+3(3a)(-1)2+(-1)3
Multiply 32 by 3.
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Raise 3 to the power of 1.
27a3+32⋅31a2⋅-1+3(3a)(-1)2+(-1)3
Use the power rule aman=am+n to combine exponents.
27a3+32+1a2⋅-1+3(3a)(-1)2+(-1)3
27a3+32+1a2⋅-1+3(3a)(-1)2+(-1)3
Add 2 and 1.
27a3+33a2⋅-1+3(3a)(-1)2+(-1)3
27a3+33a2⋅-1+3(3a)(-1)2+(-1)3
Raise 3 to the power of 3.
27a3+27a2⋅-1+3(3a)(-1)2+(-1)3
Multiply -1 by 27.
27a3-27a2+3(3a)(-1)2+(-1)3
Multiply 3 by 3.
27a3-27a2+9a(-1)2+(-1)3
Raise -1 to the power of 2.
27a3-27a2+9a⋅1+(-1)3
Multiply 9 by 1.
27a3-27a2+9a+(-1)3
Raise -1 to the power of 3.
27a3-27a2+9a-1
27a3-27a2+9a-1
Simplify (3a-1)^3

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