What is expand (y(y+1)^3)/3 ?

The solution to expand (y(y+1)^3)/3 is (y^4)/3+y^3+y^2+y/3

Popular >

expand (y(y+1)^3)/3

expand

\frac{y ( y + 1 ) ^{3}}{3}

\frac{y ^{4}}{3} + y^{3} + y^{2} + \frac{y}{3}

Solution steps

\frac{y ( y + 1 ) ^{3}}{3}

(y + 1)^{3} = y^{3} + 3 y^{2} + 3 y + 1

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

Expand

y (y^{3} + 3 y^{2} + 3 y + 1) : y^{4} + 3 y^{3} + 3 y^{2} + y

= \frac{y ^{4} + 3 y ^{3} + 3 y ^{2} + y}{3}

Apply the fraction rule:

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

\frac{y ^{4} + 3 y ^{3} + 3 y ^{2} + y}{3} = \frac{y ^{4}}{3} + \frac{3 y ^{3}}{3} + \frac{3 y ^{2}}{3} + \frac{y}{3}

= \frac{y ^{4}}{3} + \frac{3 y ^{3}}{3} + \frac{3 y ^{2}}{3} + \frac{y}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{y ^{4}}{3} + y^{3} + y^{2} + \frac{y}{3}

\frac{4 f - y}{4 ( 1 + c )}

\frac{11 u ^{2} + 18 u + 5}{u ( 3 u + 1 )}

\frac{f ( x ^{2} - 5 + h ) - x ^{2} - 5}{h}

ln (t) (t ln (t) - t)

\frac{1}{s ( s ^{s} + 2 s + 2 )}

What is expand (y(y+1)^3)/3 ?
The solution to expand (y(y+1)^3)/3 is (y^4)/3+y^3+y^2+y/3