(a+8)^2 - 2(a+8)(b-2) + (a-2)^2
Expanding the terms:
(a+8)(a+8) - 2(a+8)(b-2) + (a-2)(a-2)
(a^2 + 8a + 8a + 64) - 2(ab - 2a + 8b - 16) + (a^2 - 2a - 2a + 4)
(a^2 + 16a + 64) - 2ab + 4a + 16b - 32 + a^2 - 4a + 4
Combine like terms:
2a^2 + 16a + 64 - 2ab + 4a + 16b - 32 - 4a + 4
2a^2 + 16a + 4a - 4a + 64 - 32 + 4 - 2ab + 16b
2a^2 + 16a + 2ab - 16b + 36
Therefore, (a+8)^2 - 2(a+8)(b-2) + (a-2)^2 is equal to 2a^2 + 16a + 2ab - 16b + 36.
(a+8)^2 - 2(a+8)(b-2) + (a-2)^2
Expanding the terms:
(a+8)(a+8) - 2(a+8)(b-2) + (a-2)(a-2)
(a^2 + 8a + 8a + 64) - 2(ab - 2a + 8b - 16) + (a^2 - 2a - 2a + 4)
(a^2 + 16a + 64) - 2ab + 4a + 16b - 32 + a^2 - 4a + 4
Combine like terms:
2a^2 + 16a + 64 - 2ab + 4a + 16b - 32 - 4a + 4
2a^2 + 16a + 4a - 4a + 64 - 32 + 4 - 2ab + 16b
2a^2 + 16a + 2ab - 16b + 36
Therefore, (a+8)^2 - 2(a+8)(b-2) + (a-2)^2 is equal to 2a^2 + 16a + 2ab - 16b + 36.