Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Use an area model to multiply polynomials and combine like terms
Problem
Complete the displayed area model for \((x~+~3)(x~+~4)\). Report the \(\text{four}~\text{cells}\) in row-major order—top-left, top-right, bottom-left, bottom-right—and give the combined product.
The area model organizes the same pairwise multiplication as distribution. Each cell comes from multiplying its row label by its column label, so we’ll fill the four cells in the requested order, add their areas, and combine the two linear cell expressions to form one polynomial.
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