What is expand ((x+h)y^3-(x+h)^3y)/h ?

The solution to expand ((x+h)y^3-(x+h)^3y)/h is (xy^3)/h+y^3-(x^3y)/h-3x^2y-3hxy-h^2y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ((x+h)y^3-(x+h)^3y)/h

expand

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

\frac{x y ^{3}}{h} + y^{3} - \frac{x ^{3} y}{h} - 3 x^{2} y - 3 h x y - h^{2} y

Solution steps

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

(x + h)^{3} = x^{3} + 3 h x^{2} + 3 h^{2} x + h^{3}

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

Expand

(x + h) y^{3} - (x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3}) y : x y^{3} + h y^{3} - x^{3} y - 3 h x^{2} y - 3 h^{2} x y - h^{3} y

= \frac{x y ^{3} + h y ^{3} - x ^{3} y - 3 h x ^{2} y - 3 h ^{2} x y - h ^{3} y}{h}

Apply the fraction rule:

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

\frac{x y ^{3} + h y ^{3} - x ^{3} y - 3 h x ^{2} y - 3 h ^{2} x y - h ^{3} y}{h} = \frac{x y ^{3}}{h} + \frac{h y ^{3}}{h} - \frac{x ^{3} y}{h} - \frac{3 h x ^{2} y}{h} - \frac{3 h ^{2} x y}{h} - \frac{h ^{3} y}{h}

= \frac{x y ^{3}}{h} + \frac{h y ^{3}}{h} - \frac{x ^{3} y}{h} - \frac{3 h x ^{2} y}{h} - \frac{3 h ^{2} x y}{h} - \frac{h ^{3} y}{h}

\frac{h y ^{3}}{h} = y^{3}

\frac{3 h x ^{2} y}{h} = 3 x^{2} y

\frac{3 h ^{2} x y}{h} = 3 h x y

\frac{h ^{3} y}{h} = h^{2} y

= \frac{x y ^{3}}{h} + y^{3} - \frac{x ^{3} y}{h} - 3 x^{2} y - 3 h x y - h^{2} y

8 (6 - 4)

\frac{( x + 4 ) ^{4}}{4}

(x^{\frac{4}{5}} + y^{\frac{4}{5}})^{2}

\frac{( ( 2 x - 5 ) ( x + 2 ) )}{( x + 1 )}

ln (\frac{x - 1}{x})

What is expand ((x+h)y^3-(x+h)^3y)/h ?
The solution to expand ((x+h)y^3-(x+h)^3y)/h is (xy^3)/h+y^3-(x^3y)/h-3x^2y-3hxy-h^2y