`a,` Sửa đề: `(x^3 + x^2y + xy^2 + y^3)(x - y) = x^4 - y^4`
`VT = (x^3 + x^2y + xy^2 + y^3)(x - y)`
`= x^4 - x^3y + x^3y - x^2y^2 + x^2y^2 - xy^3 + xy^3 - y^4`
`= x^4 - y^4 = VP` (đpcm)
`b, a^3 + b^3 = (a + b). [(a - b)^2 + ab]`
`VP = (a + b). [(a - b)^2 + ab]`
`= (a + b). [a^2 - 2ab + b^2 + ab]`
`= (a + b). [a^2 - ab+ b^2]`
`= a^3 - a^2b + ab^2 + a^2b - ab^2 + b^3`
`= a^3 + b^3 = VT` (đpcm)
`c, x^2 + 4x + 4 ≥ 0`
`VT = x^2 + 2. x. 2 + 2^2`
`= (x + 2)^2`
Mà `(x + 2)^2 ≥ 0 ⇒ x^2 + 4x + 4 ≥ 0` (đpcm)
`d, x^2 - 6x + 11 > 0`
`VT = (x^2 - 6x + 9) + 2`
`= (x^2 - 2. x. 3 + 3^2) + 2`
`= (x - 3)^2 + 2`
Mà `(x + 3)^2 ≥ 0 ⇒ (x - 3)^2 + 2 ≥ 2`
`⇒ (x^2 - 6x + 9) + 2 ≥ 0` (đpcm)
