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

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Answer 1 · 2018-03-02T13:41:31

$x^3 + 3x^2 +3x + 1$

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

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

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