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

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

Evaluate

$$1-x^{4}$$

Solution Steps

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

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

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.

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

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

$$1-x^{4}$$

Expand

$$1-x^{4}$$

Solution Steps

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

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

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.

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

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

$$1-x^{4}$$