Generic Rectangle Calculator
Use the area model to multiply binomials of the form (ax+b)(cx+d)
Enter the coefficients for (ax+b)(cx+d):
What is the Generic Rectangle Method?
The generic rectangle (or area model) is a visual method for multiplying binomials. It represents the multiplication as the area of a rectangle, with each side representing one of the binomials. The four cells inside the rectangle represent the partial products.
How to Use the Generic Rectangle Method
To multiply binomials using the generic rectangle method:
- Write one binomial across the top of the rectangle (cx + d)
- Write the other binomial along the left side (ax + b)
- Fill in each cell by multiplying the terms from the corresponding row and column
- Add all the products to find the expanded form
Benefits of the Area Model
- Visually represents multiplication of polynomials
- Helps beginners understand the process of polynomial multiplication
- Can be extended to multiply larger polynomials
- Useful for factoring quadratic expressions
- Connects algebraic operations to geometric concepts
Example
Multiply (2x + 3)(x + 4) using the generic rectangle:
Step 1: Create a rectangle with (2x + 3) on the left and (x + 4) on top.
Step 2: Fill in the cells:
- 2x × x = 2x²
- 2x × 4 = 8x
- 3 × x = 3x
- 3 × 4 = 12
Step 3: Combine like terms: 2x² + 8x + 3x + 12 = 2x² + 11x + 12