Fundamental Concepts

83. Area of the Whole · Visualizing polynomial multiplication

The total area equals the sum of the four sub-rectangle areas.

w₁w₂h₁h₂(w₁+w₂)(h₁+h₂)w₁h₁+w₂h₁+w₁h₂+w₂h₂w₁ = 200w₁ = 200w₂ = 300w₂ = 300h₁ = 150h₁ = 150h₂ = 200h₂ = 200w₁h₁ = 30000w₁h₁ = 30000w₂h₁ = 45000w₂h₁ = 45000w₁h₂ = 40000w₁h₂ = 40000w₂h₂ = 60000w₂h₂ = 60000Total area = 175000Total area = 175000
Multiplying two binomials (a + b)(c + d) gives four products — ac, ad, bc, bd. The area-model rectangle shows them as four sub-areas whose sum equals the total area (a+b)(c+d).
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