Solve a*a^7-a^4*a

$$a \cdot a ^ { 7 } - a ^ { 4 } \cdot a$$

Evaluate

$$\left(a^{3}-1\right)a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$a^{8}-a^{4}a$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$a^{8}-a^{5}$$

Factor

$$\left(a-1\right)\left(a^{2}+a+1\right)a^{5}$$

Solution Steps

Factor out a^{4}.

$$a^{4}\left(\frac{a^{7}}{a^{3}}-a\right)$$

Consider a^{4}-a. Factor out a.

$$a\left(a^{3}-1\right)$$

Consider a^{3}-1. Rewrite a^{3}-1 as a^{3}-1^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

$$\left(a-1\right)\left(a^{2}+a+1\right)$$

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

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