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# What is the expansion of (x + 1)^4?

Sep 24, 2016

${\left(x + 1\right)}^{4} = {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4 x + 1$

#### Explanation:

According to Binomial Theorem expansion of ${\left(x + a\right)}^{n}$ is

x^n+nx^(n-1)a+(n(n-1))/(2!)x^(n-2)a^2+(n(n-1)(n-3))/(3!)x^(n-3)a^3+(n(n-1)(n-3)(n-4))/(4!)x^(n-4)a^4+.....+a^n

Hence ${\left(x + 1\right)}^{4} = {x}^{4} + 4 {x}^{3} \times 1 + \frac{4 \times 3}{2 \times 1} {x}^{2} \times {1}^{2} + \frac{4 \times 3 \times 2}{3 \times 2 \times 1} x \times {1}^{3} + \frac{4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} {1}^{4}$

= ${x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4 x + 1$