Solve 2cf^4-2ck^4

$$2 c f ^ { 4 } - 2 c k ^ { 4 }$$

Factor

$$2c\left(f-k\right)\left(f+k\right)\left(f^{2}+k^{2}\right)$$

Solution Steps

Factor out 2.

$$2\left(cf^{4}-ck^{4}\right)$$

Consider cf^{4}-ck^{4}. Factor out c.

$$c\left(f^{4}-k^{4}\right)$$

Consider f^{4}-k^{4}. Rewrite f^{4}-k^{4} as \left(f^{2}\right)^{2}-\left(k^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(f^{2}-k^{2}\right)\left(f^{2}+k^{2}\right)$$

Consider f^{2}-k^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(f-k\right)\left(f+k\right)$$

Rewrite the complete factored expression.

$$2c\left(f-k\right)\left(f+k\right)\left(f^{2}+k^{2}\right)$$

Evaluate

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