What is expand (1+2x)^8 ?

The solution to expand (1+2x)^8 is 1+16x+112x^2+448x^3+1120x^4+1792x^5+1792x^6+1024x^7+256x^8

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expand (1+2x)^8

expand

(1 + 2 x)^{8}

1 + 16 x + 112 x^{2} + 448 x^{3} + 1120 x^{4} + 1792 x^{5} + 1792 x^{6} + 1024 x^{7} + 256 x^{8}

Solution steps

(1 + 2 x)^{8}

Apply binomial theorem:

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

a = 1, b = 2 x

= i = 0 \sum 8 (i 8) \cdot 1^{(8 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (2 x)^{0} : 1

Simplify

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

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} (2 x)^{2} : 112 x^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (2 x)^{3} : 448 x^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (2 x)^{4} : 1120 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (2 x)^{5} : 1792 x^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (2 x)^{6} : 1792 x^{6}

Simplify

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

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (2 x)^{8} : 256 x^{8}

= 1 + 16 x + 112 x^{2} + 448 x^{3} + 1120 x^{4} + 1792 x^{5} + 1792 x^{6} + 1024 x^{7} + 256 x^{8}

2 0^{- 1}

(- t^{7}) (- t^{5})

5 \cdot (- 9)

\frac{csc ( θ ) - sin ( θ )}{cos ( θ )}

\frac{24 x ^{3} y ^{5} z ^{6}}{8 z ^{4} x ^{9} y ^{6}}

What is expand (1+2x)^8 ?
The solution to expand (1+2x)^8 is 1+16x+112x^2+448x^3+1120x^4+1792x^5+1792x^6+1024x^7+256x^8