Example1. Expand `(x+2)^4`
Solution:
`(x+2)^4`
Using Binomial Theorem,
`(a+b)^n=((n),(0))a^nb^0+((n),(1))a^(n-1)b^1+((n),(2))a^(n-2)b^2+...+((n),(n))a^0b^n`
where `((n),(0))=1,((n),(1))=n,((n),(n))=1,((n),(r))=(n!)/(r!(n-r)!)`
`"Here "a=x,b=2,n=4`
`=((4),(0))(x)^4(2)^0+((4),(1))(x)^3(2)^1+((4),(2))(x)^2(2)^2+((4),(3))(x)^1(2)^3+((4),(4))(x)^0(2)^4`
`=1(x)^4(2)^0+4(x)^3(2)^1+(4!)/(2!(4-2)!)(x)^2(2)^2+(4!)/(3!(4-3)!)(x)^1(2)^3+1(x)^0(2)^4`
`=1(x^4)(1)+4(x^3)(2)+(4*3)/(2*1)(x^2)(4)+(4)/(1)(x)(8)+1(1)(16)`
`=1(x^4)(1)+4(x^3)(2)+6(x^2)(4)+4(x)(8)+1(1)(16)`
`=x^4+8x^3+24x^2+32x+16`
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