Question

How do you use the binomial formula to expand `(x+1)^3`?

Answer 1

`x^3 + 3x^2 +3x + 1`

Explanation:

Binomial formula for `(a+b)^3`

`=> ^3C_0a^3b^0 + ^3C_1a^2b^1 +^3C_2a^1b^2 + ^3C_3a^0b^3`

Here, `a = x` and `b = 1`.

`=> ^3C_0x^3 + ^3C_1x^2xx1^1 +^3C_2x^1xx1^2 + ^3C_3xx1^3`

As `color(red)(->^3C_0=^3C_3=1) and color(magenta)(->^3C_1=^3C_2 = 3`

`=> x^3 + 3x^2 +3x + 1`