Simplify (3x-1)^7

(3x-1)7
Use the Binomial Theorem.
(3x)7+7(3x)6⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Simplify each term.
Apply the product rule to 3x.
37×7+7(3x)6⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 7.
2187×7+7(3x)6⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Apply the product rule to 3x.
2187×7+7(36×6)⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 6.
2187×7+7(729×6)⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 729 by 7.
2187×7+5103×6⋅-1+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply -1 by 5103.
2187×7-5103×6+21(3x)5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Apply the product rule to 3x.
2187×7-5103×6+21(35×5)(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 5.
2187×7-5103×6+21(243×5)(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 243 by 21.
2187×7-5103×6+5103×5(-1)2+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise -1 to the power of 2.
2187×7-5103×6+5103×5⋅1+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 5103 by 1.
2187×7-5103×6+5103×5+35(3x)4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Apply the product rule to 3x.
2187×7-5103×6+5103×5+35(34×4)(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 4.
2187×7-5103×6+5103×5+35(81×4)(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 81 by 35.
2187×7-5103×6+5103×5+2835×4(-1)3+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise -1 to the power of 3.
2187×7-5103×6+5103×5+2835×4⋅-1+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply -1 by 2835.
2187×7-5103×6+5103×5-2835×4+35(3x)3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Apply the product rule to 3x.
2187×7-5103×6+5103×5-2835×4+35(33×3)(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 3.
2187×7-5103×6+5103×5-2835×4+35(27×3)(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 27 by 35.
2187×7-5103×6+5103×5-2835×4+945×3(-1)4+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Raise -1 to the power of 4.
2187×7-5103×6+5103×5-2835×4+945×3⋅1+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Multiply 945 by 1.
2187×7-5103×6+5103×5-2835×4+945×3+21(3x)2(-1)5+7(3x)(-1)6+(-1)7
Apply the product rule to 3x.
2187×7-5103×6+5103×5-2835×4+945×3+21(32×2)(-1)5+7(3x)(-1)6+(-1)7
Raise 3 to the power of 2.
2187×7-5103×6+5103×5-2835×4+945×3+21(9×2)(-1)5+7(3x)(-1)6+(-1)7
Multiply 9 by 21.
2187×7-5103×6+5103×5-2835×4+945×3+189×2(-1)5+7(3x)(-1)6+(-1)7
Raise -1 to the power of 5.
2187×7-5103×6+5103×5-2835×4+945×3+189×2⋅-1+7(3x)(-1)6+(-1)7
Multiply -1 by 189.
2187×7-5103×6+5103×5-2835×4+945×3-189×2+7(3x)(-1)6+(-1)7
Multiply 3 by 7.
2187×7-5103×6+5103×5-2835×4+945×3-189×2+21x(-1)6+(-1)7
Raise -1 to the power of 6.
2187×7-5103×6+5103×5-2835×4+945×3-189×2+21x⋅1+(-1)7
Multiply 21 by 1.
2187×7-5103×6+5103×5-2835×4+945×3-189×2+21x+(-1)7
Raise -1 to the power of 7.
2187×7-5103×6+5103×5-2835×4+945×3-189×2+21x-1
2187×7-5103×6+5103×5-2835×4+945×3-189×2+21x-1
Simplify (3x-1)^7