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

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

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expand (2x+1)^8

expand

(2 x + 1)^{8}

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

Solution steps

(2 x + 1)^{8}

Apply binomial theorem:

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

a = 2 x, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{15}{4} \div \frac{1}{5}

+ x^{2} - 100

1 \frac{20}{100}

x^{2} \cdot + x^{3}

- 3 \cdot (- 6)

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