what is the completely factored form of $x^{2}-16xy + 64y^{2}$?\n$xy(x - 16 + 64y)$\n$xy(x + 16 + 64y)$\n$(x…

Explanation:

Step1: Recall the perfect - square trinomial formula

The perfect - square trinomial formula is (a^{2}-2ab + b^{2}=(a - b)^{2}). In the given expression (x^{2}-16xy + 64y^{2}), we have (a=x) and (b = 8y) since (2ab=2\times x\times8y = 16xy) and (b^{2}=(8y)^{2}=64y^{2}).

Step2: Factor the trinomial

Using the perfect - square trinomial formula (a^{2}-2ab + b^{2}=(a - b)^{2}), substituting (a=x) and (b = 8y) into it, we get (x^{2}-16xy + 64y^{2}=(x - 8y)^{2}=(x - 8y)(x - 8y)).

Answer:

C. ((x - 8y)(x - 8y))