a) \((x + 3)(x^2 - 3x + 9) - (54 + x^3)\)
\(= ( x + 3)(x^2 - 3.x + 3^2) - (54 + x^3)\)
\(= x^3 + 3^3 - (54 + x^3)\)
\(= x^3 + 27 - 54 - x^3\)
\(= -27\)
b) \((2x + y)(4x^2 - 2xy + y^2) - (2x - y)(4x^2 + 2xy + y^2)\)
\(= (2x + y)[(2x)^2 - 2x.y + y^2] - (2x - y)[(2x)^2 + 2x.y + y^2]\)
\(= [(2x)^3 + y^3] - [(2x)^3 - y^3]\)
\(= (2x)^3 + y^3 - (2x)^3 + y^3\)
\(= 2y^3\)
Lưu ý: \(+ \,\,\,\, a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\ + \,\,\, a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)
