What is expand (1+3x)^7 ?

The solution to expand (1+3x)^7 is 1+21x+189x^2+945x^3+2835x^4+5103x^5+5103x^6+2187x^7

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expand (1+3x)^7

expand

(1 + 3 x)^{7}

1 + 21 x + 189 x^{2} + 945 x^{3} + 2835 x^{4} + 5103 x^{5} + 5103 x^{6} + 2187 x^{7}

Solution steps

(1 + 3 x)^{7}

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 7 (i 7) \cdot 1^{(7 - i)} (3 x)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 1^{7} (3 x)^{0} : 1

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 1^{6} (3 x)^{1} : 21 x

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 1^{5} (3 x)^{2} : 189 x^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 1^{4} (3 x)^{3} : 945 x^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 1^{3} (3 x)^{4} : 2835 x^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 1^{2} (3 x)^{5} : 5103 x^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 1^{1} (3 x)^{6} : 5103 x^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 1^{0} (3 x)^{7} : 2187 x^{7}

= 1 + 21 x + 189 x^{2} + 945 x^{3} + 2835 x^{4} + 5103 x^{5} + 5103 x^{6} + 2187 x^{7}

\frac{400}{100}

8 \cdot 340 \cdot 3

2 \frac{π}{\frac{1}{4}}

3 x^{2} - 13 x - 30

5 \frac{1}{3} - 2 \frac{1}{2}

What is expand (1+3x)^7 ?
The solution to expand (1+3x)^7 is 1+21x+189x^2+945x^3+2835x^4+5103x^5+5103x^6+2187x^7