What is expand (x+2)^8 ?

The solution to expand (x+2)^8 is x^8+16x^7+112x^6+448x^5+1120x^4+1792x^3+1792x^2+1024x+256

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expand (x+2)^8

expand

(x + 2)^{8}

x^{8} + 16 x^{7} + 112 x^{6} + 448 x^{5} + 1120 x^{4} + 1792 x^{3} + 1792 x^{2} + 1024 x + 256

Solution steps

(x + 2)^{8}

Apply binomial theorem:

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

a = x, b = 2

= i = 0 \sum 8 (i 8) x^{(8 - i)} \cdot 2^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} \cdot 2^{0} : x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} \cdot 2^{1} : 16 x^{7}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} \cdot 2^{2} : 112 x^{6}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} \cdot 2^{3} : 448 x^{5}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} \cdot 2^{4} : 1120 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} \cdot 2^{5} : 1792 x^{3}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} \cdot 2^{6} : 1792 x^{2}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} \cdot 2^{7} : 1024 x

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} \cdot 2^{8} : 256

= x^{8} + 16 x^{7} + 112 x^{6} + 448 x^{5} + 1120 x^{4} + 1792 x^{3} + 1792 x^{2} + 1024 x + 256

8 (- 2 i) (- 5 - 4 i)

(w^{2} + 1)^{8}

4 \times 1 0^{7}

2 x (x)

- 9 + \frac{x}{7} + 4

What is expand (x+2)^8 ?
The solution to expand (x+2)^8 is x^8+16x^7+112x^6+448x^5+1120x^4+1792x^3+1792x^2+1024x+256