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Question
Expand the following (1 – x + x2)4
Solution
Put 1 – x = y.
Then (1 – x + x2)4 = (y + x2)4
= 4C0 y4(x2)0 + 4C1 y3(x2)1 + 4C2 y2(x2)2 + 4C3 y(x2)3 + 4C4 (x2)4
= y4 + 4y3 x2 + 6y2 x4 + 4y x6 + x8
= (1 – x)4 + 4x2 (1 – x)3 + 6x4 (1 – x)2 + 4x6 (1 – x) + x8
= 1 – 4x + 10x2 – 16x3 + 19x4 – 16x5 + 10x6 – 4x7 + x8
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