What is expand (x(-x+8)^4)/2 ?

The solution to expand (x(-x+8)^4)/2 is (x^5)/2-16x^4+192x^3-1024x^2+2048x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x(-x+8)^4)/2

expand

\frac{x ( - x + 8 ) ^{4}}{2}

\frac{x ^{5}}{2} - 16 x^{4} + 192 x^{3} - 1024 x^{2} + 2048 x

Solution steps

\frac{x ( - x + 8 ) ^{4}}{2}

(- x + 8)^{4} = x^{4} - 32 x^{3} + 384 x^{2} - 2048 x + 4096

= \frac{x ( x ^{4} - 32 x ^{3} + 384 x ^{2} - 2048 x + 4096 )}{2}

Expand

x (x^{4} - 32 x^{3} + 384 x^{2} - 2048 x + 4096) : x^{5} - 32 x^{4} + 384 x^{3} - 2048 x^{2} + 4096 x

= \frac{x ^{5} - 32 x ^{4} + 384 x ^{3} - 2048 x ^{2} + 4096 x}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{5} - 32 x ^{4} + 384 x ^{3} - 2048 x ^{2} + 4096 x}{2} = \frac{x ^{5}}{2} - \frac{32 x ^{4}}{2} + \frac{384 x ^{3}}{2} - \frac{2048 x ^{2}}{2} + \frac{4096 x}{2}

= \frac{x ^{5}}{2} - \frac{32 x ^{4}}{2} + \frac{384 x ^{3}}{2} - \frac{2048 x ^{2}}{2} + \frac{4096 x}{2}

\frac{32 x ^{4}}{2} = 16 x^{4}

\frac{384 x ^{3}}{2} = 192 x^{3}

\frac{2048 x ^{2}}{2} = 1024 x^{2}

\frac{4096 x}{2} = 2048 x

= \frac{x ^{5}}{2} - 16 x^{4} + 192 x^{3} - 1024 x^{2} + 2048 x

\frac{6.106 N \cdot 20 m}{0.31 m ^{2} \cdot 2 \cdot 1 0 ^{11}}

(6 y - 12 x^{2} z) a t (2, - 1, 0)

\frac{2 x y ( y ^{3} - 1 )}{3 + 3 x ^{2}}

A (- 2, 3) y B (6, - 1)

lo g_{10} (x^{3} y - 12)

What is expand (x(-x+8)^4)/2 ?
The solution to expand (x(-x+8)^4)/2 is (x^5)/2-16x^4+192x^3-1024x^2+2048x