Solve 13y^4-y^3-y^2/y^2

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

Evaluate

$$13\left(y^{2}-y-1\right)$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{4}-y^{3}-y^{2}}{y^{2}}.

$$13\times \frac{\left(y-\left(-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)y^{2}}{y^{2}}$$

Cancel out y^{2} in both numerator and denominator.

$$13\left(y-\left(-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)$$

Expand the expression.

$$13\left(y^{2}-y-1\right)$$

Use the distributive property to multiply 13 by y^{2}-y-1.

$$13y^{2}-13y-13$$

Expand

$$13y^{2}-13y-13$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{4}-y^{3}-y^{2}}{y^{2}}.

$$13\times \frac{\left(y-\left(-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)y^{2}}{y^{2}}$$

Cancel out y^{2} in both numerator and denominator.

$$13\left(y-\left(-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)\left(y-\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\right)$$

Expand the expression.

$$13\left(y^{2}-y-1\right)$$

Use the distributive property to multiply 13 by y^{2}-y-1.

$$13y^{2}-13y-13$$