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Popular Algebra >

expand (5x^2+1)^{10}

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Solution

expand (5x2+1)10

Solution

9765625x20+19531250x18+17578125x16+9375000x14+3281250x12+787500x10+131250x8+15000x6+1125x4+50x2+1
Solution steps
(5x2+1)10
Apply binomial theorem: (a+b)n=i=0∑n​(in​)a(n−i)bia=5x2,b=1
=i=0∑10​(i10​)(5x2)(10−i)⋅1i
Expand summation
=0!(10−0)!10!​(5x2)10⋅10+1!(10−1)!10!​(5x2)9⋅11+2!(10−2)!10!​(5x2)8⋅12+3!(10−3)!10!​(5x2)7⋅13+4!(10−4)!10!​(5x2)6⋅14+5!(10−5)!10!​(5x2)5⋅15+6!(10−6)!10!​(5x2)4⋅16+7!(10−7)!10!​(5x2)3⋅17+8!(10−8)!10!​(5x2)2⋅18+9!(10−9)!10!​(5x2)1⋅19+10!(10−10)!10!​(5x2)0⋅110
Simplify 0!(10−0)!10!​(5x2)10⋅10:9765625x20
Simplify 1!(10−1)!10!​(5x2)9⋅11:19531250x18
Simplify 2!(10−2)!10!​(5x2)8⋅12:17578125x16
Simplify 3!(10−3)!10!​(5x2)7⋅13:9375000x14
Simplify 4!(10−4)!10!​(5x2)6⋅14:3281250x12
Simplify 5!(10−5)!10!​(5x2)5⋅15:787500x10
Simplify 6!(10−6)!10!​(5x2)4⋅16:131250x8
Simplify 7!(10−7)!10!​(5x2)3⋅17:15000x6
Simplify 8!(10−8)!10!​(5x2)2⋅18:1125x4
Simplify 9!(10−9)!10!​(5x2)1⋅19:50x2
Simplify 10!(10−10)!10!​(5x2)0⋅110:1
=9765625x20+19531250x18+17578125x16+9375000x14+3281250x12+787500x10+131250x8+15000x6+1125x4+50x2+1

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