To show x²-8x+16 as a perfect square in a visual model, a square of which side should be made?

Correct answer: x-4

The direct answer is B: x-4. Use the identity (x-a)²=x²-2ax+a². Since the constant term is 16=4², the small square has side 4. The negative middle term is -8x=-2·4·x, so the cross-rectangles are subtracted and the complete square is (x-4)²=x²-8x+16. Option A, (x+4)², would produce a positive middle term +8x. Option C, (x-8)², would produce -16x and a constant term 64. Option D, (x+8)², would produce +16x and 64. The sign of the middle term determines whether the model uses addition or subtraction. Memory cue: a negative middle term means the smaller side is subtracted; half of 8 gives 4, so the side is x-4.