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Subtraction of Algebraic Expressions

What should b...

Question

What should be added to $1 - x + x^{2} - 2 x^{3}$ to get $x^{3}$ ?
(2 marks)

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Solution

Let, the term to be added be y.
$\Rightarrow 1 - x + x^{2} - 2 x^{3} + y = x^{3}$
$\Rightarrow y = x^{3} - (1 - x + x^{2} - 2 x^{3})$ (1 mark)
$= x^{3} - 1 + x - x^{2} + 2 x^{3}$
$= 3 x^{3} - x^{2} + x - 1$ .
Hence, $y$ = $3 x^{3} - x^{2} + x - 1$ .
(1 mark)

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