Đáp án:
`3,`
`a, A = (x + 2)^2 - (2x -1)^2`
`= x^2 + 2.x.2 + 2^2 - [(2x)^2 - 2.2x.1 + 1^2]`
`= x^2 + 4x + 4 - 4x^2 + 4x - 1`
`= (x^2 - 4x^2) + (4x + 4x) + (4 - 1)`
`= -3x^2 + 8x + 3`
`b, 2(x + 1)^2 - (2x - 3)(x + 1)`
`= 2(x^2 + 2x + 1) - (2x^2 + 2x - 3x - 3)`
`= 2x^2 + 4x + 2 - 2x^2 - 2x + 3x + 3`
`= (2x^2 - 2x^2) + (4x - 2x + 3x) + (2 + 3)`
`= 5x + 5`
`c, (3x + 2)^2 - (x^2 - x - 3)2x`
`= (3x)^2 + 2.3x.2 + 2^2 - 2x^3 + 2x^2 + 6x`
`= 9x^2 + 12x + 4 - 2x^3 + 2x^2 + 6x`
`= (9x^2 + 2x^2) - 2x^3 + (12x + 6x) + 4`
`= 11x^2 - 2x^3 + 18x + 4`
`4,`
`a, M = (2a + 1)^2 - (1 - 2a)^2`
`= (2a)^2 + 2.2a.1 + 1^2 - [1^2 - 2.1.2a + (2a)^2]`
`= 4a^2 + 4a + 1 - 1 + 4a - 4a^2`
`= (4a^2 - 4a^2) + (4a + 4a) + (1 - 1)`
`= 8a`
`b, N = (a + 2y)^2 - 2(a + 2y)(2y - 1) + (2y - 1)^2`
`= [(a + 2y) - (2y - 1)]^2`
`= (a + 2y - 2y + 1)^2`
`= (a + 1)^2`
`= a^2 + 2a + 1`
`c, A = (x - y)^2 + 4xy`
`= x^2 - 2xy + y^2 + 4xy`
`= x^2 + (-2xy + 4xy) + y^2`
`= x^2 + 2xy + y^2`
`= (x + y)^2`
