Simplify: $(2 x + 1) (1 - x) (x^{2} + x)$

2 x^{4} - x^{3} + 2 x^{2} + x

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- 2 x^{4} - x^{3} + 2 x^{2} + x

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- 2 x^{4} + x^{3} + 2 x^{2} + x

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- 2 x^{4} - x^{3} + 2 x^{2} - x

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Solution

The correct option is B $- 2 x^{4} - x^{3} + 2 x^{2} + x$
$(2 x + 1) (1 - x) (x^{2} + x)$
Multiply the coefficients and add the exponents of the variable.
$=$ $(2 x + 1) (x^{2} + x - x^{3} - x^{2})$
$=$ $2 x^{3} + 2 x^{2} - 2 x^{4} - 2 x^{3} + x^{2} + x - x^{3} - x^{2}$
$=$ $- 2 x^{4} - x^{3} + 2 x^{2} + x$

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