Simplifying
2[a(a + b) + b(a + b)]
2[(a * a + b * a) + b(a + b)]

Reorder the terms:
2[(ab + a2) + b(a + b)]
2[(ab + a2) + b(a + b)]
2[ab + a2 + (a * b + b * b)]
2[ab + a2 + (ab + b2)]

Reorder the terms:
2[ab + ab + a2 + b2]

Combine like terms: ab + ab = 2ab
2[2ab + a2 + b2]
[2ab * 2 + a2 * 2 + b2 * 2]
[4ab + 2a2 + 2b2]