What is expand (x-3)^8 ?

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

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expand (x-3)^8

expand

(x - 3)^{8}

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

Solution steps

(x - 3)^{8}

Apply binomial theorem:

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

a = x, b = - 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

4 \times (- x)

\frac{3}{4 2}

\frac{8 x y ^{8}}{4 x ^{6} y ^{7}}

\frac{2}{x} + \frac{3 x - 2}{x + 1}

\frac{100}{5}

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