Use the BODMAS rule to simplify the expression:
$x y^{2} + x^{3} - x [x^{2} - x] [2 x] + (x - 1) x^{2}$

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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

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Solution

The correct option is D $- x^{4} + 4 x^{3} - x^{2} + x y^{2}$
$x y^{2} + x^{3} - x [x^{2} - x] [2 x] + (x - 1) x^{2}$
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.
$=$ $x y^{2} + x^{3} + [- x^{3} + x^{2}] 2 x + x^{3} - x^{2}$
$=$ $x y^{2} + x^{3} - x^{4} + 2 x^{3} + x^{3} - x^{2}$
$=$ $x y^{2} + 4 x^{3} - x^{4} - x^{2}$
$=$ $- x^{4} + 4 x^{3} - x^{2} + x y^{2}$

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