Subjects algebra

Rectangle Products 73F93C

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1. **State the problem:** We are given a rectangle divided into four smaller rectangles with terms along the sides: $7z$ and $-4$ on one side, and $7z$ and $4$ on the other side. We want to fill in the missing two boxes representing the products of these terms. 2. **Recall the distributive property:** When multiplying binomials, each term in the first binomial multiplies each term in the second binomial. The products fill the smaller rectangles. 3. **Known products:** - Top left box: $7z \times 7z = 49z^2$ - Bottom right box: $-4 \times 4 = -16$ 4. **Find missing products:** - Top right box: $7z \times 4 = 28z$ - Bottom left box: $-4 \times 7z = -28z$ 5. **Summary:** The four boxes are: $$ \begin{array}{|c|c|} \hline 49z^2 & 28z \\ \hline -28z & -16 \\ \hline \end{array} $$ These complete the rectangle and represent the product of the binomials $(7z - 4)(7z + 4)$. 6. **Final answer:** The missing boxes are $28z$ and $-28z$.