Simplify: $3 x [x^{2} + 1] - [2 x (x^{2} + x - 1) + 1] - x^{2}$

x^{3} - 3 x^{2} + x + 1

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x^{3} - 3 x^{2} + 5 x - 1

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x^{3} + x^{2} - 5 x + 1

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x^{3} + 3 x^{2} + 5 x - 1

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Solution

The correct option is A $x^{3} - 3 x^{2} + 5 x - 1$
$3 x [x^{2} + 1] - [2 x (x^{2} + x - 1) + 1] - x^{2}$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$3 x [x^{2} + 1] - [2 x (x^{2} + x - 1) + 1] - x^{2}$
$=$ $3 x . x^{2} + 3 x .1 - [2 x . x^{2} + 2 x . x - 2 x .1 + 1] - x^{2}$
$=$ $3 x^{3} + 3 x - 2 x^{3} - 2 x^{2} + 2 x - 1 - x^{2}$
$=$ $x^{3} - 3 x^{2} + 5 x - 1$

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(x^{3} - 3 x^{2} + 5 x - 1)

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

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