Solve (c^4+d^2)(d^2-c^4)

$$( c ^ { 4 } + d ^ { 2 } ) ( d ^ { 2 } - c ^ { 4 } )$$

Evaluate

$$d^{4}-c^{8}$$

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}.

$$\left(d^{2}\right)^{2}-\left(c^{4}\right)^{2}$$

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

$$d^{4}-\left(c^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$d^{4}-c^{8}$$

Expand

$$d^{4}-c^{8}$$

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}.

$$\left(d^{2}\right)^{2}-\left(c^{4}\right)^{2}$$

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

$$d^{4}-\left(c^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$d^{4}-c^{8}$$