Get the solution to "Does x3−x2 equal x2? How can I prove..."

Sahar Bowden

Answered question

2022-02-28

Does

x^{3} - x^{2}

equal

x^{2}

? How can I prove so, mathematically?

Athena Hussain

Beginner2022-03-01Added 5 answers

Step 1
$x^{3} - x^{2} = x^{2}$
$\Rightarrow x^{3} - 2 x^{2} = 0$
$∴ x^{2} (x - 2) = 0$
So now there are two valid solutions.
$x^{2} = 0$

$∴ x = 0$
or,
$x - 2 = 0$
$∴ x = 2$
So the solution are $x = 0, 2$

lilwayne10j6o

Beginner2022-03-02Added 8 answers

Step 1
Generally, no.

x^{3} - x^{2} \neq x^{2}

To be fair, if x equals 0 or 2, then it would seem they are valid.

0 - 0 = 0 \Rightarrow 0^{3} - 0^{2} = 0

8 - 4 = 4 \Rightarrow 2^{3} - 2^{2} = 2^{2}

But in a general sense, your question is false.

x^{3} - x^{2} = x^{2} (x - 1)

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