1. The problem is to find which area model represents the expression $ (2x + 3)(3x + 3) $. 2. The formula to expand this product is the distributive property: $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. Applying this to $ (2x + 3)(3x + 3) $, we multiply each term in the first binomial by each term in the second binomial: $$ 2x \times 3x = 6x^2 $$ $$ 2x \times 3 = 6x $$ $$ 3 \times 3x = 3x \times 3 = 9x $$ $$ 3 \times 3 = 9 $$ 4. Adding all these parts together: $$ 6x^2 + 6x + 9x + 9 = 6x^2 + 15x + 9 $$ 5. Now, let's analyze the area models: - The first graph has 4 rows and 5 columns, with 3 columns of $x^2$ squares and 2 columns of $x$ rectangles in the first three rows, and some 1s and $x$s in the last two rows. - The second graph has 4 rows and 6 columns, with 2 columns of $x^2$ squares and 3 columns of $x$ rectangles in the first three rows. 6. Since the expanded expression has $6x^2$, we expect 6 squares labeled $x^2$ in the area model. - The first graph has 3 columns of $x^2$ squares in 3 rows, which is $3 \times 3 = 9$ squares, but the description says the first three columns in rows 1-3 have blue squares labeled $x^2$. - The second graph has 2 columns of $x^2$ squares in 3 rows, which is $2 \times 3 = 6$ squares. 7. The second graph matches the $6x^2$ term. 8. For the $15x$ term, the second graph has 3 columns of $x$ rectangles in 3 rows, which is $3 \times 3 = 9$ rectangles, but the description is incomplete for the last row. 9. The first graph has 2 columns of $x$ rectangles in the first three rows and 2 columns of $x$ rectangles in the last two rows, totaling $2 \times 3 + 2 \times 2 = 6 + 4 = 10$ rectangles, which does not match $15x$. 10. Therefore, the second graph better represents the expression $ (2x + 3)(3x + 3) $ because it has $6x^2$ squares and more $x$ rectangles closer to $15x$. Final answer: The second graph (bottom-left) represents the expression $ (2x + 3)(3x + 3) $.