What is expand ((x(2-2x)^3))/2 ?

The solution to expand ((x(2-2x)^3))/2 is -4x^4+12x^3-12x^2+4x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ((x(2-2x)^3))/2

expand

\frac{( x ( 2 - 2 x ) ^{3} )}{2}

- 4 x^{4} + 12 x^{3} - 12 x^{2} + 4 x

Solution steps

\frac{x ( 2 - 2 x ) ^{3}}{2}

(2 - 2 x)^{3} = 8 - 24 x + 24 x^{2} - 8 x^{3}

= \frac{x ( - 8 x ^{3} + 24 x ^{2} - 24 x + 8 )}{2}

Factor

8 - 24 x + 24 x^{2} - 8 x^{3} : 8 (1 - 3 x + 3 x^{2} - x^{3})

= \frac{x \cdot 8 ( 1 - 3 x + 3 x ^{2} - x ^{3} )}{2}

Divide the numbers:

\frac{8}{2} = 4

= 4 x (- x^{3} + 3 x^{2} - 3 x + 1)

Distribute parentheses

= 4 x (- x^{3}) + 4 x \cdot 3 x^{2} + 4 x (- 3 x) + 4 x \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - 4 x^{3} x + 4 \cdot 3 x^{2} x - 4 \cdot 3 xx + 4 \cdot 1 \cdot x

Simplify

- 4 x^{3} x + 4 \cdot 3 x^{2} x - 4 \cdot 3 xx + 4 \cdot 1 \cdot x : - 4 x^{4} + 12 x^{3} - 12 x^{2} + 4 x

= - 4 x^{4} + 12 x^{3} - 12 x^{2} + 4 x

e x (e^{2} x + 3 e x + 9)

\frac{( 3 x + 1 ) ( x + 2 )}{2}

d (3 x y + e^{y})

\frac{2 ^{3}}{2 ^{5}}

\frac{32 x}{( x ^{2} + 3 ) ^{2}}

What is expand ((x(2-2x)^3))/2 ?
The solution to expand ((x(2-2x)^3))/2 is -4x^4+12x^3-12x^2+4x