What is expand (1+3x)^8 ?

The solution to expand (1+3x)^8 is 1+24x+252x^2+1512x^3+5670x^4+13608x^5+20412x^6+17496x^7+6561x^8

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expand (1+3x)^8

expand

(1 + 3 x)^{8}

1 + 24 x + 252 x^{2} + 1512 x^{3} + 5670 x^{4} + 13608 x^{5} + 20412 x^{6} + 17496 x^{7} + 6561 x^{8}

Solution steps

(1 + 3 x)^{8}

Apply binomial theorem:

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

a = 1, b = 3 x

= i = 0 \sum 8 (i 8) \cdot 1^{(8 - i)} (3 x)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (3 x)^{0} : 1

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} (3 x)^{1} : 24 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} (3 x)^{2} : 252 x^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (3 x)^{3} : 1512 x^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (3 x)^{4} : 5670 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (3 x)^{5} : 13608 x^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (3 x)^{6} : 20412 x^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} (3 x)^{7} : 17496 x^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (3 x)^{8} : 6561 x^{8}

= 1 + 24 x + 252 x^{2} + 1512 x^{3} + 5670 x^{4} + 13608 x^{5} + 20412 x^{6} + 17496 x^{7} + 6561 x^{8}

1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16}

(x - 1) \times (x - 2)

3 a^{2} - 3 a - 36

\frac{3}{( \frac{3}{x} )}

(- 2 x + 7) (x^{2} + 2 x - 4)

What is expand (1+3x)^8 ?
The solution to expand (1+3x)^8 is 1+24x+252x^2+1512x^3+5670x^4+13608x^5+20412x^6+17496x^7+6561x^8