What is the value of the following expression?
$(1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 - x)$

1 + x^{16}

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1 - x^{16}

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x^{16} - 1

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x^{8} + 1

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Solution

The correct option is B $1 - x^{16}$
$(1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 - x)$
$\Rightarrow (1 - x^{2}) (1 + x^{2}) (1 + x^{4}) (1 + x^{8})$
$\Rightarrow (1 - x^{4}) (1 + x^{4}) (1 + x^{8})$
$\Rightarrow (1 - x^{8}) (1 + x^{8})$
$\Rightarrow (1 - x^{16})$

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1 + x + x^{2} + . . . x^{p} = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8})

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1 + x + x^{2} + . . . . x^{p} = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8})

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