How do you use the binomial theorem to expand and simplify the expression $(1-2x)^3$ ?

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Answer 1 · 2018-03-22T12:51:32

$(1-2x)^3 = 1-6x+12x^2-8x^3$

We know $(a+b)^n= nC_0 a^n*b^0 +nC_1 a^(n-1)*b^1 + nC_2 a^(n-2)*b^2+..........+nC_n a^(n-n)*b^n$

Here $a=1,b=-2x ,n=3$ We know, $nC_r = (n!)/(r!*(n-r)!$

$:.3C_0 =1 , 3C_1 =3, 3C_2 =3,3C_3 =1$

$:.(1-2x)^3$

$= 3C_0*1^3+3C_1*1^2*(-2x)+3C_2*1*(-2x)^2+3C_3*(-2x)^3$

$:.(1-2x)^3 = 1-6x+12x^2-8x^3$ [Ans]

How do you use the binomial theorem to expand and simplify the expression (1-2x)^3(1-2x)^3?