Cho x + 3.y – 4 = 0, tính x^3 - x^2 + 9.x^2.y - 9.y^2 + 27.x.y^2 + 27.y^3 - 6.x.y
Đề bài. Cho x + 3y – 4 = 0, tính x3 - x2 + 9x2y - 9y2 + 27xy2 + 27y3 - 6xy
Ta có:
x3 - x2 + 9x2y - 9y2 + 27xy2 + 27y3 - 6xy
= x3 + 3x2y – 4x2 + 3x2 + 9xy – 12x + 6x2y + 18xy2 – 24xy + 9xy2 + 27y3 – 36y2 + 9xy + 27y2 + 12x
= x2(x + 3y – 4) + 3x(x + 3y – 4) + 6xy(x + 3y – 4) + 9y2(x + 3y – 4) + 9y(x + 3y) + 12x
= 0 + 0 + 0 + 0 + 0 + 9y.4 + 12x
= 36y + 12x
= 12(x + 3y)
= 12.4
= 48.