1. Section 4.1
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By adding the areas of the smaller rectangles we get the area of the model. This is the same as the product of its sides. (2x-3)(4x+1)=8x^2+2x-12x-3 ⇓ (2x-3)(4x+1)=8x^2-10x-3 To verify Casey's pattern we will multiply the expressions across the diagonals of the rectangle.
(4x-8)^2=(4x-8)(4x-8) Now we can create our area model.
Let's calculate the products.
By adding the areas of the smaller rectangles we get the area of the model. This is the same as the product of its sides. (4x-8)^2=16x^2+(- 32x)+(- 32x)+64 ⇓ (4x-8)^2=16x^2-64x+64 To verify Casey's pattern we will multiply the expressions across the diagonals of the rectangle.
- a(- b)=a* b
Multiply