Solve (4)a^4-(1-a)(1+a)(1+a^2)

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

Evaluate

$$5a^{4}-1$$

Solution Steps

Use the distributive property to multiply 1-a by 1+a and combine like terms.

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

Consider \left(1-a^{2}\right)\left(1+a^{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To find the opposite of 1-a^{4}, find the opposite of each term.

$$4a^{4}-1+a^{4}$$

Combine 4a^{4} and a^{4} to get 5a^{4}.

$$5a^{4}-1$$

Expand

$$5a^{4}-1$$

Solution Steps

Use the distributive property to multiply 1-a by 1+a and combine like terms.

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

Consider \left(1-a^{2}\right)\left(1+a^{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To find the opposite of 1-a^{4}, find the opposite of each term.

$$4a^{4}-1+a^{4}$$

Combine 4a^{4} and a^{4} to get 5a^{4}.

$$5a^{4}-1$$