What is expand r^2+(g^3-8)^5 ?

The solution to expand r^2+(g^3-8)^5 is r^2+g^{15}-40g^{12}+640g^9-5120g^6+20480g^3-32768

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expand r^2+(g^3-8)^5

expand

r^{2} + (g^{3} - 8)^{5}

r^{2} + g^{15} - 40 g^{12} + 640 g^{9} - 5120 g^{6} + 20480 g^{3} - 32768

Solution steps

r^{2} + (g^{3} - 8)^{5}

Apply binomial theorem:

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

a = g^{3}, b = - 8

= i = 0 \sum 5 (i 5) (g^{3})^{(5 - i)} (- 8)^{i}

Expand summation

= r^{2} + \frac{5 !}{0 ! ( 5 - 0 ) !} (g^{3})^{5} (- 8)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (g^{3})^{4} (- 8)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (g^{3})^{3} (- 8)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (g^{3})^{2} (- 8)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (g^{3})^{1} (- 8)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (g^{3})^{0} (- 8)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (g^{3})^{5} (- 8)^{0} : g^{15}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (g^{3})^{4} (- 8)^{1} : - 40 g^{12}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (g^{3})^{3} (- 8)^{2} : 640 g^{9}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (g^{3})^{2} (- 8)^{3} : - 5120 g^{6}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (g^{3})^{1} (- 8)^{4} : 20480 g^{3}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (g^{3})^{0} (- 8)^{5} : - 32768

= r^{2} + g^{15} - 40 g^{12} + 640 g^{9} - 5120 g^{6} + 20480 g^{3} - 32768

\frac{14 - 30}{2 ( - 4 )}

2.2 \cdot 1 0^{5}

\frac{x ^{2} - x - 30}{x ^{2} - 25}

- \frac{4}{3} \cdot (- 2)

\frac{73}{6}

What is expand r^2+(g^3-8)^5 ?
The solution to expand r^2+(g^3-8)^5 is r^2+g^{15}-40g^{12}+640g^9-5120g^6+20480g^3-32768