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Expand of the expression : (1-2x)^5...

Expand of the expression : `(1-2x)^5`

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`(1-2x)^5`
`=overset(5)underset(r=0)(Sigma).^(5)C_(r)(1)^(5-r)(-2x)^(r)`
`=^(5)C_(0).1^(5)+^(5)C_(1).1^(4).(-2x)^(1)+^(5)C_(2).1^(3).(-2x)^(2)`
`+^(5)C_(3).1^(2)(-2x)^(3)+^(5)C_(4).1(-2x)^(4)+^(5)C_(5).(-2x)^(5)`
`=1+5(-2x)+10(4x^(2))+10(-8x^(3))+5(16x^(4))`
`+1.(-32x^(5))`
`=1-10x+40x^(2)-80x^(3)+80x^(4)-32x^(5)`
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Knowledge Check

  • When x=5 and y=2 , the expression (xy)/(70)+(9)/(5(x+y))+(1)/(x+y)=?

    A
    `(19)/(35)`
    B
    `(58)/(105)`
    C
    `(1)/(2)`
    D
    `(4)/(7)`
  • The value of the expression (5)/(3)x^(3)+1 when x=-2 is

    A
    `-(37)/(3)`
    B
    `-(7)/(3)`
    C
    `(20)/(3)`
    D
    `(23)/(3)`
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