For all values of y, let $y ⋆$ be defined by $y ⋆ = y^{2} - 1$ . Which of the following is equal to $(y ⋆) ⋆$ ?

y^{4} - 1

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y^{4} - Y^{2} - 1

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y^{4} + y^{2} - 1

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y^{4} - 2 y^{2}

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y^{4} - 2 y^{2} + 1

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Solution

The correct option is B $y^{4} - 2 y^{2}$
Given y $⋆ = y^{2} - 1$
$(y^{2} - 1)$ $⋆ = (y^{2} - 1)^{2} - 1$ = $y^{4} - 2 y^{2} + 1 - 1$ = $y^{4} - 2 y^{2}$
Option C

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