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

Mar 2, 2018

${x}^{3} + 3 {x}^{2} + 3 x + 1$

Explanation:

Binomial formula for ${\left(a + b\right)}^{3}$

${\implies}^{3} {C}_{0} {a}^{3} {b}^{0} {+}^{3} {C}_{1} {a}^{2} {b}^{1} {+}^{3} {C}_{2} {a}^{1} {b}^{2} {+}^{3} {C}_{3} {a}^{0} {b}^{3}$

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

${\implies}^{3} {C}_{0} {x}^{3} {+}^{3} {C}_{1} {x}^{2} \times {1}^{1} {+}^{3} {C}_{2} {x}^{1} \times {1}^{2} {+}^{3} {C}_{3} \times {1}^{3}$

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

$\implies {x}^{3} + 3 {x}^{2} + 3 x + 1$