a) Ta có:
\(\eqalign{
& 27{x^3} + {y^3} \cr
& = {\left( {3x} \right)^3} + {y^3} \cr
& = \left( {3x + y} \right)\left[ {{{\left( {3x} \right)}^2} - 3x.y + {y^2}} \right] \cr
& = \left( {3x + y} \right)(9{x^2} - 3xy + {y^2}) \cr} \)
Suy ra:
\(\left( {3x + y} \right)(\)\(9{x^2} - 3xy + {y^2}\)\() = 27{x^3} + {y^3}\)
b) Ta có:
\(\eqalign{
& 8{x^3} - 125 \cr
& = {\left( {2x} \right)^3} - {5^3} \cr
& = \left( {2x - 5} \right)\left[ {{{\left( {2x} \right)}^2} + 2x.5 + {5^2}} \right] \cr
& = \left( {2x - 5} \right)(4{x^2} + 10x + 25) \cr} \)
Suy ra:
\(( 2x -\)\( 5\)\( )(\)\(4{x^2}\)\( + 10x +\)\( 25\)\() = 8{x^3} - 125\)
