Why negative multiplied by negative is positive?

Solution :

Let a and b be any two real numbers.

Consider the number x defined by

$x = ab + (-a)(b) + (-a)(-b)$.

We can write

$x = ab + (-a)[ (b) + (-b) ]$

  $= ab + (-a)(0)$

  $= ab + 0$

  $= ab$.

Also,

$x = [ a + (-a) ]b + (-a)(-b)$

  $= 0 \times b + (-a)(-b)$

  $= 0 + (-a)(-b)$

  $= (-a)(-b)$.

So we have $x = ab$ and $x = (-a)(-b)$

Therefore, $ab = (-a) (-b)$

Hence, negative times negative is positive.

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Updated on: 10-Oct-2022

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