Solve y^6*y^4-y^5

$$y ^ { 6 } \times y ^ { 4 } - y ^ { 5 }$$

Factor

$$\left(y-1\right)\left(y^{4}+y^{3}+y^{2}+y+1\right)y^{5}$$

Solution Steps

Factor out y^{5}.

$$y^{5}\left(yy^{4}-1\right)$$

Consider y^{5}-1. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -1 and q divides the leading coefficient 1. One such root is 1. Factor the polynomial by dividing it by y-1.

$$\left(y-1\right)\left(y^{4}+y^{3}+y^{2}+y+1\right)$$

Rewrite the complete factored expression. Polynomial y^{4}+y^{3}+y^{2}+y+1 is not factored since it does not have any rational roots.

$$y^{5}\left(y-1\right)\left(y^{4}+y^{3}+y^{2}+y+1\right)$$

Evaluate

$$y^{5}\left(y^{5}-1\right)$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$y^{10}-y^{5}$$