A square model has outer side (2x+3y+z). What is the total area of only the two rectangle pairs involving z with 2x and 3y?

Correct answer: 4xz+6yz; both symmetric pairs

Correct answer: B. In the square identity for three parts, every pair of different side components creates two symmetric rectangles. The pair 2x and z contributes 2(2x)(z)=4xz. The pair 3y and z contributes 2(3y)(z)=6yz. Adding only these requested pairs gives 4xz+6yz. Option A counts one rectangle for each pair and therefore gives only half of each contribution. Option C multiplies all three components and produces xyz, which is not the area of either requested pair. Option D wrongly includes the z² corner square and an unsupported three-factor term; the question asks only for rectangles involving z with 2x and 3y. Memory cue: in a square expansion, a pair of different parts appears twice, while a single part’s corner square appears once.