How do you multiply $(mn - 5)(mn - 5)(mn - 5)$ ?

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Answer 1 · 2015-04-22T23:24:59

If you know the identity $(a - b)^3$ ,
then you don't have to multiply.

$(a - b)^3 = a^3 - 3a^2*b + 3a*b^2 - b^3$

$(mn - 5)^3 = m^3*n^3 - 15 m^2*n^2 + 75mn - 125$

If you don't remember the Identity, then you may multiply:
$(mn - 5)^2*(mn - 5)$

$= (m^2n^2 - 10mn + 25)(mn - 5)$

$= m^3*n^3 - 15m^2*n^2 + 75*mn - 125$

How do you multiply (mn - 5)(mn - 5)(mn - 5)(mn - 5)(mn - 5)(mn - 5)?