Question

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

Answer 1

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

Explanation:

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]