Solve x=(y(y+1)(2y+1)1/6-1)

$$x=(y(y+1)(2y+1) \frac{ 1 }{ 6 } -1)$$

Solve for x

$$x=\frac{y\left(y+1\right)\left(2y+1\right)-6}{6}$$

Solution Steps

Use the distributive property to multiply y by y+1.

$$x=\left(y^{2}+y\right)\left(2y+1\right)\times \frac{1}{6}-1$$

Use the distributive property to multiply y^{2}+y by 2y+1 and combine like terms.

$$x=\left(2y^{3}+3y^{2}+y\right)\times \frac{1}{6}-1$$

Use the distributive property to multiply 2y^{3}+3y^{2}+y by \frac{1}{6}.

$$x=\frac{1}{3}y^{3}+\frac{1}{2}y^{2}+\frac{1}{6}y-1$$