Đáp án:
`a, (x + 2y + 3z)(x - 2y + 3z)`
`= (x + 3z + 2y)(x + 3z - 2y)`
`= (x + 3z)^2 - (2y)^2`
`= x^2 + 2.x.3y + (3y)^2 - (2y)^2`
`= x^2 + 6xy + 9y^2 - 4y^2`
`= x^2 + 6xy + 5y^2`
`b, (x - 1)(x^2 + x + 1)(x + 1)(x^2 + x + 1)`
`= (x^3 - 1^3)(x + 1)(x^2 + x + 1)`
`= (x^4 + x^3 - x - 1)(x^2 + x + 1)`
`= x^6 + x^5 + x^4 + x^5 + x^4 + x^3 - x^3 - x^2 - x - x^2 - x - 1`
`= x^6 + (x^5 + x^5) + (x^4 + x^4) + (x^3 - x^3) + (-x^2 - x^2) + (-x - x) - 1`
`= x^6 + 2x^5 + 2x^4 - 2x^2 - 2x - 1`
`c, (x + y)^3 - (x - y)^3`
`= x^3 + 3x^2 y + 3xy^2 + y^3 - (x^3 - 3x^2 y + 3xy^2 - y^3)`
`= x^3 + 3x^2 y + 3xy^2 + y^3 - x^3 + 3x^2 y - 3xy^2 + y^3`
`= (x^3 - x^3) + (3x^2 y + 3x^2 y) + (3xy^2 - 3xy^2) + (y^3 + y^3)`
`= 6x^2 y + 2y^3`
`d, (x^2 + 3x + 1)^2 + (3x + 1)^2 - 2(x^2 + 3x + 1)(3x + 1)`
`= (x^2 + 3x + 1)^2 - 2(x^2 + 3x + 1)(3x + 1) + (3x + 1)^2`
`= [(x^2 + 3x + 1) - (3x + 1)]^2`
`= (x^2 + 3x + 1 - 3x - 1)^2`
`= (x^2)^2`
`= x^4`
`e, (2x + 3)^2 + (2x - 3)^2 - 2(4x^2 - 9)`
`= (2x + 3)^2 - 2[(2x)^2 - 3^2] + (2x - 3)^2`
`= (2x + 3)^2 - 2(2x - 3)(2x + 3) + (2x - 3)^2`
`= [(2x + 3) - (2x - 3)]^2`
`= (2x + 3 - 2x + 3)^2`
`= 6^2`
`= 36`
`f, (x + 2)^3 + (x - 2)^3 + x^3 - 3x(x + 2)(x - 2)`
`= x^3 + 3.x^2 .2 + 3.x.2^2 + 2^3 + x^3 - 3.x^2 .2 + 3.x.2^2 - 2^3 + x^3 - 3x(x^2 - 2^2)`
`= x^3 + 6x^2 + 12x + 8 + x^3 - 6x^2 + 12x - 8 + x^3 - 3x^3 + 12x`
`= (x^3 + x^3 + x^3 - 3x^3) + (6x^2 - 6x^2) + (12x + 12x + 12x) + (8 - 8)`
`= 36x`
