What is expand (6(x^2+x)^4)/(2x^3-3x^2) ?

The solution to expand (6(x^2+x)^4)/(2x^3-3x^2) is (6x^6+24x^5+36x^4+24x^3+6x^2)/(2x-3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (6(x^2+x)^4)/(2x^3-3x^2)

expand

\frac{6 ( x ^{2} + x ) ^{4}}{2 x ^{3} - 3 x ^{2}}

\frac{6 x ^{6} + 24 x ^{5} + 36 x ^{4} + 24 x ^{3} + 6 x ^{2}}{2 x - 3}

Solution steps

\frac{6 ( x ^{2} + x ) ^{4}}{2 x ^{3} - 3 x ^{2}}

Factor

6 (x^{2} + x)^{4} : 6 x^{4} (x + 1)^{4}

= \frac{6 x ^{4} ( x + 1 ) ^{4}}{2 x ^{3} - 3 x ^{2}}

Factor out common term

x^{2} : x^{2} (2 x - 3)

= \frac{6 x ^{4} ( x + 1 ) ^{4}}{x ^{2} ( 2 x - 3 )}

Cancel

\frac{6 x ^{4} ( x + 1 ) ^{4}}{x ^{2} ( 2 x - 3 )} : \frac{6 x ^{2} ( x + 1 ) ^{4}}{2 x - 3}

= \frac{6 x ^{2} ( x + 1 ) ^{4}}{2 x - 3}

(x + 1)^{4} = x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

= \frac{6 x ^{2} ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )}{2 x - 3}

Expand

6 x^{2} (x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1) : 6 x^{6} + 24 x^{5} + 36 x^{4} + 24 x^{3} + 6 x^{2}

= \frac{6 x ^{6} + 24 x ^{5} + 36 x ^{4} + 24 x ^{3} + 6 x ^{2}}{2 x - 3}

\frac{d ^{2}}{d t ^{2}} ((s) (5 t^{3} + 3 t^{5}))

(x + 3)^{16}

e^{x} (x - y^{2} + 4 y)

cos (\frac{( n + 1 ) π}{2})

\frac{s - 6}{s ^{2} ( s + 3 )}

What is expand (6(x^2+x)^4)/(2x^3-3x^2) ?
The solution to expand (6(x^2+x)^4)/(2x^3-3x^2) is (6x^6+24x^5+36x^4+24x^3+6x^2)/(2x-3)