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

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

Factor

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

Solution Steps

Consider c^{4}-2c^{2}d^{2}+d^{4} as a polynomial over variable c.

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

Find one factor of the form c^{k}+m, where c^{k} divides the monomial with the highest power c^{4} and m divides the constant factor d^{4}. One such factor is c^{2}-d^{2}. Factor the polynomial by dividing it by this factor.

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

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

$$\left(c-d\right)\left(c+d\right)$$

Rewrite the complete factored expression.

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

Evaluate

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