What is expand (x-x^7)^4 ?

The solution to expand (x-x^7)^4 is x^4-4x^{10}+6x^{16}-4x^{22}+x^{28}

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expand (x-x^7)^4

expand

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

x^{4} - 4 x^{10} + 6 x^{16} - 4 x^{22} + x^{28}

Solution steps

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

Apply binomial theorem:

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

a = x, b = - x^{7}

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- x^{7})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- x^{7})^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- x^{7})^{1} : - 4 x^{10}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- x^{7})^{2} : 6 x^{16}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- x^{7})^{3} : - 4 x^{22}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- x^{7})^{4} : x^{28}

= x^{4} - 4 x^{10} + 6 x^{16} - 4 x^{22} + x^{28}

\frac{2}{3} + \frac{4}{11}

- 8 \times 7

(5 - 7 i) (5 + 7 i)

+ 25 6^{\frac{3}{8}}

What is expand (x-x^7)^4 ?
The solution to expand (x-x^7)^4 is x^4-4x^{10}+6x^{16}-4x^{22}+x^{28}