Step 1 of 8
Read
Read the two symbolic parts that make each edge.
Interactive lessonTopic 2274
(a + b)³
Build the identity
Partitioned cube · 1 · 3 · 3 · 1
A = ?
B = ?
Outside = ×1
Volume model
(A + B) × (A + B) × (A + B) = (A + B)³
Each edge is split into A and B.
A cube with side length A plus B, partitioned into eight rectangular prisms The eight volumes group into one A cubed, three A squared B, three A B squared, and one B cubed.
Exploded slightly so all 8 parts can be seen · diagram not to scale
1 × A³3 × A²B3 × AB²1 × B³
1 part · AAA
A × A × A = A³
3 parts · AAB · ABA · BAA
3(A × A × B) = 3A²B
3 parts · ABB · BAB · BBA
3(A × B × B) = 3AB²
1 part · BBB
B × B × B = B³
Add the volumes of all 8 parts(A + B)³ = A³ + 3A²B + 3AB² + B³
Substitute A and B into the volume identity
Volume check · set every variable to 1
Final answer
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