Solve for X: Perfect Square (x-4)² Equals Product (x+2)(x-1)

Solve for x:

$(x-4)^2=(x+2)(x-1)$

Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:

$(a+b)(c+d)=ac+ad+bc+bd$We'll use the shortened multiplication formula for a squared binomial:

$(a\pm b)^2=a^2\pm2ab+b^2$We'll therefore apply the law and formula mentioned and open the parentheses in the expressions in the equation:

$(x-4)^2=(x+2)(x-1) \\ x^2-2\cdot x\cdot4+4^2=x^2-x+2x-2 \\ x^2-8x+16=x^2+x-2$We'll continue and combine like terms, by moving terms between sides - we can notice that the squared term cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2-8x+16=x^2+x-2\\ -9x=-18\hspace{8pt}\text{/}:(-9)\\ \boxed{x=2}$Therefore the correct answer is answer A.