Solve (b^6-1)(b^6+1)=

$$( b ^ { 6 } - 1 ) ( b ^ { 6 } + 1 ) =$$

Evaluate

$$b^{12}-1$$

Solution Steps

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.

$$\left(b^{6}\right)^{2}-1$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$b^{12}-1$$

Expand

$$b^{12}-1$$

Solution Steps

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.

$$\left(b^{6}\right)^{2}-1$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$b^{12}-1$$