What is expand (x+1)^8 ?

The solution to expand (x+1)^8 is x^8+8x^7+28x^6+56x^5+70x^4+56x^3+28x^2+8x+1

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expand (x+1)^8

expand

(x + 1)^{8}

x^{8} + 8 x^{7} + 28 x^{6} + 56 x^{5} + 70 x^{4} + 56 x^{3} + 28 x^{2} + 8 x + 1

Solution steps

(x + 1)^{8}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = 1

= i = 0 \sum 8 (i 8) x^{(8 - i)} \cdot 1^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} \cdot 1^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} \cdot 1^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} \cdot 1^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} \cdot 1^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} \cdot 1^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} \cdot 1^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} \cdot 1^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} \cdot 1^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} \cdot 1^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} \cdot 1^{0} : x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} \cdot 1^{1} : 8 x^{7}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} \cdot 1^{2} : 28 x^{6}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} \cdot 1^{3} : 56 x^{5}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} \cdot 1^{4} : 70 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} \cdot 1^{5} : 56 x^{3}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} \cdot 1^{6} : 28 x^{2}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} \cdot 1^{7} : 8 x

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} \cdot 1^{8} : 1

= x^{8} + 8 x^{7} + 28 x^{6} + 56 x^{5} + 70 x^{4} + 56 x^{3} + 28 x^{2} + 8 x + 1

(x - 9) + (3 x - x^{2})

(2)^{2} + (2)^{2}

\frac{x + 7}{x ^{2} - 49}

lo g_{0.2} (5)

e^{\frac{1}{( x - y )}}

What is expand (x+1)^8 ?
The solution to expand (x+1)^8 is x^8+8x^7+28x^6+56x^5+70x^4+56x^3+28x^2+8x+1