Solve a^2-d^2+n^2-c^2-2an-2cd=

$$a ^ { 2 } - d ^ { 2 } + n ^ { 2 } - c ^ { 2 } - 2 a n - 2 c d =$$

Factor

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

Solution Steps

Rewrite a^{2}-d^{2}+n^{2}-c^{2}-2an-2cd as \left(a-n\right)^{2}-\left(d+c\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Reorder the terms.

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

Evaluate

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