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Evaluate the expression (y+1)4 – (y-1)4.

Evaluate the expression (y+1)4 – (y-1)4. Correct Answer 8(y3 + y1)

By using Binomial theorem,the expression (y+1)4 – (y-1)4 can be expanded as = (y+1)4 = 4C0y4 + 4C1y3 + 4C2y2 + 4C3y1 + 4C4y0 and (y-1)4 = 4C0y4 – 4C1y3 + 4C2y2 – 4C3y1 + 4C4y0. Now, (y+1)4 – (y-1)4 = (4C0y4 + 4C1y3 + 4C2y2 + 4C3y1 + 4C4y0) – (4C0y4 – 4C1y3 + 4C2y2 – 4C3y1 + 4C4y0) = 2(4C1y3 + 4C3y1) = 8(y3 + y1).

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