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Generic Rectangle Calculator
Area model for polynomial multiplication
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📐Generic Rectangle Method
Step 1: Create Grid
Draw rectangle with terms on sides
Rows for first, columns for second
Step 2: Multiply
Fill each cell with product
Row term × column term
Step 3: Collect
Add all products from cells
Sum represents total area
Step 4: Simplify
Combine like terms
Final polynomial form
💼Applications
Education
• Visual learning
• Area models
• Understanding distributive property
Algebra
• Polynomial multiplication
• Expanding expressions
• Alternative to FOIL
Geometry
• Area calculations
• Rectangle dimensions
• Visual proofs
💡Why "Generic Rectangle"?
The Generic Rectangle (or Area Model) visualizes polynomial multiplication as finding the area of a rectangle.
Just as the area of a rectangle is length × width, the product of two polynomials can be found by creating a grid where:
- Terms of first polynomial label the rows (height)
- Terms of second polynomial label the columns (width)
- Each cell contains the product of its row and column terms
- The sum of all cells gives the total "area" (product)