What area is formed by joining an x by x square and an x by 8 rectangle?

Correct answer: x²+8x

Direct answer: A, x²+8x. The area of the x by x square is x×x=x². The area of the x by 8 rectangle is x×8=8x. When the two non-overlapping pieces are joined, their areas add, giving x²+8x. B is wrong because it treats 8 as though it were a side of an 8 by 8 square; the rectangle has dimensions x and 8, so its area is 8x, not 64. C reverses the multiplication incorrectly and also makes the square contribution wrong. D adds the side lengths rather than calculating areas and therefore has the wrong type of quantity. A useful check is to assign x=2: the separate areas are 4 and 16, whose sum is 20; x²+8x also gives 20. Memory cue: square area is side squared, while rectangle area is length times width.