What is expand (x-8)^4 ?

The solution to expand (x-8)^4 is x^4-32x^3+384x^2-2048x+4096

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expand (x-8)^4

expand

(x - 8)^{4}

x^{4} - 32 x^{3} + 384 x^{2} - 2048 x + 4096

Solution steps

(x - 8)^{4}

Apply binomial theorem:

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

a = x, b = - 8

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- 8)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 8)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 8)^{1} : - 32 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 8)^{2} : 384 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 8)^{3} : - 2048 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 8)^{4} : 4096

= x^{4} - 32 x^{3} + 384 x^{2} - 2048 x + 4096

18 x^{4} y^{7}

- 7 + (- 11)

- 11 + (- 8)

lo g_{4} (81) - lo g_{2} (3)

a \cdot 1

What is expand (x-8)^4 ?
The solution to expand (x-8)^4 is x^4-32x^3+384x^2-2048x+4096