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Simplifying
(ab + bc)(ab + bc)

Multiply (ab + bc) * (ab + bc)
(ab(ab + bc) + bc(ab + bc))
((ab * ab + bc * ab) + bc(ab + bc))

Reorder the terms:
((ab2c + a2b2) + bc(ab + bc))
((ab2c + a2b2) + bc(ab + bc))
(ab2c + a2b2 + (ab * bc + bc * bc))
(ab2c + a2b2 + (ab2c + b2c2))

Reorder the terms:
(ab2c + ab2c + a2b2 + b2c2)

Combine like terms: ab2c + ab2c = 2ab2c
(2ab2c + a2b2 + b2c2)
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