Solve -(y^2+y-3)^2/2-2

$$- \frac { ( y ^ { 2 } + y - 3 ) ^ { 2 } } { 2 } - 2$$

Expand

$$-\frac{y^{4}}{2}-y^{3}+\frac{5y^{2}}{2}+3y-\frac{13}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

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

Since -\frac{\left(y^{2}+y-3\right)^{2}}{2} and \frac{2\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -\left(y^{2}+y-3\right)^{2}-2\times 2.

$$\frac{-y^{4}-y^{3}+3y^{2}-y^{3}-y^{2}+3y+3y^{2}+3y-9-4}{2}$$

Combine like terms in -y^{4}-y^{3}+3y^{2}-y^{3}-y^{2}+3y+3y^{2}+3y-9-4.

$$\frac{-y^{4}-2y^{3}+5y^{2}+6y-13}{2}$$

Evaluate

$$-\frac{\left(y^{2}+y-3\right)^{2}}{2}-2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

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

Since -\frac{\left(y^{2}+y-3\right)^{2}}{2} and \frac{2\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -\left(y^{2}+y-3\right)^{2}-2\times 2.

$$\frac{-y^{4}-y^{3}+3y^{2}-y^{3}-y^{2}+3y+3y^{2}+3y-9-4}{2}$$

Combine like terms in -y^{4}-y^{3}+3y^{2}-y^{3}-y^{2}+3y+3y^{2}+3y-9-4.

$$\frac{-y^{4}-2y^{3}+5y^{2}+6y-13}{2}$$