(x – 3)4 = (x – 3)(x – 3)(x – 3)(x – 3)
= (x·x – x·3 – 3·x + 3·3)(x·x – x·3 – 3·x + 3·3)
= (x2 – 6x + 9)(x2 – 6x + 9)
= x2(x2 – 6x + 9) – 6x(x2 – 6x + 9) + 9(x2 – 6x + 9)
= x2·x2 – x2·6x + x2·9 – 6x·x2 + 6x·6x – 6x·9 + 9·x2 – 9·6x + 9·9
= x4 – 6x3 + 9x2 – 6x3 + 36x2 – 54x + 9x2 – 54x + 81
= x4 – 12x3 + 54x2 – 108x + 81
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