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Popular Algebra >

expand (3x+1)^{10}

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Solution

expand (3x+1)10

Solution

59049x10+196830x9+295245x8+262440x7+153090x6+61236x5+17010x4+3240x3+405x2+30x+1
Solution steps
(3x+1)10
Apply binomial theorem: (a+b)n=i=0∑n​(in​)a(n−i)bia=3x,b=1
=i=0∑10​(i10​)(3x)(10−i)⋅1i
Expand summation
=0!(10−0)!10!​(3x)10⋅10+1!(10−1)!10!​(3x)9⋅11+2!(10−2)!10!​(3x)8⋅12+3!(10−3)!10!​(3x)7⋅13+4!(10−4)!10!​(3x)6⋅14+5!(10−5)!10!​(3x)5⋅15+6!(10−6)!10!​(3x)4⋅16+7!(10−7)!10!​(3x)3⋅17+8!(10−8)!10!​(3x)2⋅18+9!(10−9)!10!​(3x)1⋅19+10!(10−10)!10!​(3x)0⋅110
Simplify 0!(10−0)!10!​(3x)10⋅10:59049x10
Simplify 1!(10−1)!10!​(3x)9⋅11:196830x9
Simplify 2!(10−2)!10!​(3x)8⋅12:295245x8
Simplify 3!(10−3)!10!​(3x)7⋅13:262440x7
Simplify 4!(10−4)!10!​(3x)6⋅14:153090x6
Simplify 5!(10−5)!10!​(3x)5⋅15:61236x5
Simplify 6!(10−6)!10!​(3x)4⋅16:17010x4
Simplify 7!(10−7)!10!​(3x)3⋅17:3240x3
Simplify 8!(10−8)!10!​(3x)2⋅18:405x2
Simplify 9!(10−9)!10!​(3x)1⋅19:30x
Simplify 10!(10−10)!10!​(3x)0⋅110:1
=59049x10+196830x9+295245x8+262440x7+153090x6+61236x5+17010x4+3240x3+405x2+30x+1

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