Rút gọn các biểu thức sau:
a) \((x + 3)(x^2 – 3x + 9) – (54 + x^3)\)
b) \((2x + y)(4x^2 – 2xy + y^2) – (2x – y)(4x^2 + 2xy + y^2)\)
a) \((x + 3)(x^2 – 3x + 9) – (54 + x^3) = (x + 3)(x^2 – 3x + 3^2 ) - (54 + x^3)\) \( = x3 + 3^3 - (54 + x^3) = x^3 + 27 - 54 - x^3 = -27\)
b) \((2x + y)(4x^2 – 2xy + y^2) – (2x – y)(4x^2 + 2xy + y^2)\)
\(= (2x + y)[(2x)^2 – 2 . x . y + y^2] – (2x – y)[(2x)^2 + 2 . x . y + y^2]\)\(= [(2x)^3 + y^3]- [(2x)^3 - y^3] = (2x)^3 + y^3- (2x)^3 + y^3= 2y^3 \)
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