Solve (a-1)*(a^2+1)*(a^2-a^3)

$$( a - 1 ) \cdot ( a ^ { 2 } + 1 ) \cdot ( a ^ { 2 } - a ^ { 3 } )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply a-1 by a^{2}+1.

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

Use the distributive property to multiply a^{3}+a-a^{2}-1 by a^{2}-a^{3} and combine like terms.

$$2a^{5}-a^{6}+2a^{3}-2a^{4}-a^{2}$$

Expand

$$-a^{6}+2a^{5}-2a^{4}+2a^{3}-a^{2}$$

Solution Steps

Use the distributive property to multiply a-1 by a^{2}+1.

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

Use the distributive property to multiply a^{3}+a-a^{2}-1 by a^{2}-a^{3} and combine like terms.

$$2a^{5}-a^{6}+2a^{3}-2a^{4}-a^{2}$$