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

1 Answer
Alan P.
Apr 22, 2015

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#

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