What is expand (1+2x^3)^5 ?

The solution to expand (1+2x^3)^5 is 1+10x^3+40x^6+80x^9+80x^{12}+32x^{15}

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expand (1+2x^3)^5

expand

(1 + 2 x^{3})^{5}

1 + 10 x^{3} + 40 x^{6} + 80 x^{9} + 80 x^{12} + 32 x^{15}

Solution steps

(1 + 2 x^{3})^{5}

Apply binomial theorem:

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

a = 1, b = 2 x^{3}

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (2 x^{3})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (2 x^{3})^{0} : 1

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (2 x^{3})^{1} : 10 x^{3}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (2 x^{3})^{2} : 40 x^{6}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (2 x^{3})^{3} : 80 x^{9}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (2 x^{3})^{4} : 80 x^{12}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (2 x^{3})^{5} : 32 x^{15}

= 1 + 10 x^{3} + 40 x^{6} + 80 x^{9} + 80 x^{12} + 32 x^{15}

(x + 4) (x - 2) + (x - 6) (x + 4) - 2 x^{2}

\frac{1}{x - 4} - \frac{5}{( x - 4 ) ^{3}} - \frac{2}{( x - 4 ) ^{2}}

(1 + i) (2 - i)

(2 n - 1)^{3}

\frac{1}{cos ^{2} ( θ )}

What is expand (1+2x^3)^5 ?
The solution to expand (1+2x^3)^5 is 1+10x^3+40x^6+80x^9+80x^{12}+32x^{15}