In the rectangle model, what is the expanded area represented by x(x + 9)?

Correct answer: x² + 9x

The correct answer is C: x² + 9x. The area of a rectangle is one side multiplied by the other side. Apply the distributive law to x(x + 9): multiply x by each term inside the bracket. Thus x·x + x·9 = x² + 9x. In a visual area model, the side x + 9 is split into two parts, x and 9. The rectangle with dimensions x by x has area x², while the rectangle with dimensions x by 9 has area 9x. Adding the two component areas gives x² + 9x. Option A is wrong because x·9 is 9x, not 9; the variable x cannot simply disappear. Option B reverses the roles and incorrectly creates 9x². Option D gives only the sum of the side lengths, not the area; area requires multiplication. The memory cue is: when a factor outside brackets multiplies a sum, multiply it by every term inside: a(b+c)=ab+ac. The rectangle picture is a geometric way to understand this distributive rule.