In a rectangle model for (x+4)(x+1), what is the sum of the x-terms after splitting the product into four parts?

Correct answer: 5x

Direct answer: Option B, 5x. Split the first factor into x and 4 and the second factor into x and 1. The rectangle model then has four smaller regions: x×x=x², x×1=x, 4×x=4x, and 4×1=4. The terms containing exactly x are x and 4x. Since x means 1x, these are like terms and can be combined: 1x+4x=5x. Therefore the complete product is x²+5x+4. Option A, 4x, includes only the 4-by-x rectangle and forgets the x-by-1 rectangle. Option C, x², is the quadratic term from the large x-by-x region, not the sum of the x-terms. Option D, 4, is the constant corner region and has no variable. The important rule is that like terms have the same variable raised to the same power; x and 4x are like terms, but x² and x are not. A memory cue is to inspect each rectangle before adding: variable terms come from the two cross-products.