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

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

Factor

$$\left(2-c-a\right)\left(2+c-a\right)$$

Solution Steps

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

$$\left(-2+a-c\right)\left(-2+a+c\right)$$

Reorder the terms.

$$\left(a-c-2\right)\left(a+c-2\right)$$

Evaluate

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