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

$$( 1 - a ) ( 1 - a ^ { 2 } ) + ( 1 + a ) ( 1 + a ^ { 2 } ) - 2 a ( 1 + a ) ( a - 1 )$$

Evaluate

$$2\left(a+1\right)$$

Solution Steps

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

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

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

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

Add 1 and 1 to get 2.

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

Combine -a^{2} and a^{2} to get 0.

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

Combine -a and a to get 0.

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

Combine a^{3} and a^{3} to get 2a^{3}.

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

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

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

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

$$2+2a^{3}+2a-2a^{3}$$

Combine 2a^{3} and -2a^{3} to get 0.

$$2+2a$$

Expand

$$2a+2$$

Solution Steps

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

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

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

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

Add 1 and 1 to get 2.

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

Combine -a^{2} and a^{2} to get 0.

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

Combine -a and a to get 0.

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

Combine a^{3} and a^{3} to get 2a^{3}.

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

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

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

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

$$2+2a^{3}+2a-2a^{3}$$

Combine 2a^{3} and -2a^{3} to get 0.

$$2+2a$$