Đáp án:
Giải thích các bước giải:
` a) (2x + 1)^2 +(2x + 3)^2 – 2(2x + 1)(2x + 3)`
`=(2x+1 - 2x -3)^2`
`=(-2)^2=4.`
`b) (2x – 3)(2x + 3) – (x + 5)^2 – (x – 1)(x + 2)`
`=4x^2 - 9 - x^2 - 10x -25 - x^2 -x +2`
`=2x^2 -11x - 32.`
` c) (24x^2 y^3 z^2 – 12x^3 y^2 z^3 + 36x^2 y^2 z^2) : (-6x^2 y^2 z^2)` (ĐK: `xyz \ne0`)
`=-6x^2y^2z^2( -4y + 2xz - 6) : (-6x^2 y^2 z^2)`
`= 2xz - 4y - 6.`
`d) (x + 2y)(x^2 – 2xy + 4y^2) – (x – y)(x^2 + xy + y^2)`
`= (x^3 - 8y^3) - (x^3 - y^3)`
`= x^3 - 8y^3 - x^3 + y^3`
`= 9y^3.`
`e) (x^3 + 4x^2 – x – 4) : (x + 4)` (ĐK: `xyz \ne-4`)
`=[x^2(x+4) -(x+4)] : (x+4)`
`=(x+4)(x^2-1): (x+4)`
`=(x+1)(x-1).`
`f) x^2(x + y) + y^2(x + y) + 2x^2 y + 2xy^2`
`=(x+y)(x^2+y^2) + 2xy (x+y)`
`=(x+y)(x^2+2xy+y^2)`
`=(x+y)(x+y)^2`
`=(x+y)^3.`
`g) (x + y)^2 + (x – y)^2 – 2(x + y)(x - y)`
`=(x+y -x + y)^2.`
`= (2y)^2 = 4y^2.`
`h) (a + b)^3 - (a – b)^3 – 2b^3`
`=a^3+3a^2b + 3ab^2 + b^3 - a^3+ 3a^2b - 3ab^2 + b^3 - 2b^3`
`=6a^2b.`
`i) (x-y)(x+y)(x^2+y^2)(x^4+y^4)`
`=(x^2-y^2)(x^2+y^2)(x^4+y^4)`
`= (x^4 - y^4)(x^4 + y^4)`
`=x^8 - y^8.`