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Đáp án:
$N = 1010$
Giải thích các bước giải:
$Với$ $2x - y = 9:$
$N = 8x^3 - 12x^2y + 6xy^2 - y^3 + 12x^2 - 12xy + 3y^2 + 6x - 3y + 11$
$= (8x^3 - y^3) - (12x^2y - 6xy^2) + (12x^2 - 12xy + 3y^2) + (6x - 3y) + 11$
$= (2x - y)(4x^2 + 2xy + y^2) - 6xy(2x - y) + 3(4x^2 - 4xy + y^2) + 3(2x - y) + 11$
$= (2x - y)(4x^2 + 2x + y^2 - 6xy) + 3(2x - y)^2 + 3(2x - y) + 11$
$= (2x - y)(4x^2 - 4xy + y^2) + 3(2x - y)(2x - y + 1) + 11$
$= (2x - y)(2x - y)^2 + 3(2x - y)(2x - y + 1) + 11$
$= (2x - y)^3 + 3(2x - y)(2x - y + 1) + 11$
$= 9^3 + 3.9.(9 + 1) + 11$
$= 729 + 270 + 11$
$= 1010$
