Solve a-a^2*a^3

$$a - a ^ { 2 } \times a ^ { 3 }$$

Factor

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

Solution Steps

Factor out a.

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

Consider 1-a^{4}. Rewrite 1-a^{4} as 1^{2}-\left(-a^{2}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Reorder the terms.

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

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

$$\left(1-a\right)\left(1+a\right)$$

Reorder the terms.

$$\left(-a+1\right)\left(a+1\right)$$

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

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

Evaluate

$$a-a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$a-a^{5}$$