Solve (x+4)(x-4)(x^2+16)

$$( x + 4 ) ( x - 4 ) ( x ^ { 2 } + 16 )$$

Evaluate

$$x^{4}-256$$

Solution Steps

Use the distributive property to multiply x+4 by x-4 and combine like terms.

$$\left(x^{2}-16\right)\left(x^{2}+16\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 16.

$$\left(x^{2}\right)^{2}-256$$

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

$$x^{4}-256$$

Expand

$$x^{4}-256$$

Solution Steps

Use the distributive property to multiply x+4 by x-4 and combine like terms.

$$\left(x^{2}-16\right)\left(x^{2}+16\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 16.

$$\left(x^{2}\right)^{2}-256$$

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

$$x^{4}-256$$