In the model of a square with side (3y+2), which is the largest square-type part algebraically?

Correct answer: 9y^2, the square formed by (3y)×(3y)

The direct answer is A: 9y^2. To build the area model, split the side 3y+2 into two parts, 3y and 2. The part whose length and width are both 3y is a square, so its area is (3y)(3y)=9y^2. This is the largest square-type region because 3y is the larger part of the side in the algebraic model. Option A is therefore correct. Option B, 6y, comes from the two rectangular strips: (3y)(2)+(2)(3y)=6y+6y=12y if both strips are counted; in any case it is not one square region. Thus it cannot be the requested square part. Option C is the small 2×2 corner square, whose area is 4, so it is smaller. Option D is a length, not an area, and therefore cannot represent a square-type area. Memory cue: in a square-of-a-binomial model, square each side piece first; the two variable pieces give (3y)^2=9y^2.