Solve (x^3-9)(x^3+9)+17

$$( x ^ { 3 } - 9 ) ( x ^ { 3 } + 9 ) + 17$$

Evaluate

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

Solution Steps

Consider \left(x^{3}-9\right)\left(x^{3}+9\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 9.

$$\left(x^{3}\right)^{2}-81+17$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}-81+17$$

Add -81 and 17 to get -64.

$$x^{6}-64$$

Expand

$$x^{6}-64$$

Solution Steps

Consider \left(x^{3}-9\right)\left(x^{3}+9\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 9.

$$\left(x^{3}\right)^{2}-81+17$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}-81+17$$

Add -81 and 17 to get -64.

$$x^{6}-64$$