Đáp án:
`a, (4x^2 - 4x + 1) - (x + 1)^2`
`= [(2x)^2 - 2.2x.1 + 1^2] - (x + 1)^2`
`= (2x - 1)^2 - (x + 1)^2`
`= [(2x - 1) - (x + 1)][(2x - 1) + (x + 1)]`
`= (2x - 1 - x - 1)(2x - 1 + x + 1)`
`= (x - 2).3x`
`b, x^3 + 27 = x^3 + 3^3`
`= (x + 3)(x^2 - x.3 + 3^2)`
`= (x + 3)(x^2 - 3x + 9)`
`c. x^4 + 2x^2 + 1`
`= (x^2)^2 + 2.x^2 . 1 + 1^2`
`= (x^2 + 1)^2`
`d, x^3 + 1 - x^2 - x`
`= (x^3 + 1) - (x^2 + x)`
`= (x + 1)(x^2 - x + 1) - x(x + 1)`
`= (x + 1)(x^2 - x + 1 - x)`
`= (x + 1)(x^2 - 2x + 1)`
`= (x + 1)(x - 1)^2`
`e, x^3 - 3x^2 + 3x - 1`
`= x^3 - 3.x^2 . 1 + 3.x.1^2 - 1^3`
`= (x - 1)^3`
`f, (x + y)^2 - 2(x + y) + 1`
`= (x + y)^2 - 2(x + y).1 + 1^2`
`= (x + y - 1)^2`
`g, x^4 + y^4`
`= x^4 + 2x^2 y^2 + y^4 - 2x^2 y^2`
`= (x^2)^2 + 2x^2 y^2 + (y^2)^2 - 2x^2 y^2`
`= (x^2 + y^2)^2 - (\sqrt{2xy})^2`
`= (x^2 + y^2 + \sqrt{2xy})(x^2 + y^2 - \sqrt{2xy})`
`h, x^2 - 3y^2`
`= x^2 - (\sqrt{3y})^2`
`= (x - \sqrt{3y})(x + \sqrt{3y})`
