Đáp án + Giải thích các bước giải:

`1)`

`(x-2)^2-(x-3)(x-1)`$\\$`x^{2}-4x+4-(x^{2}-x-3x+3)`$\\$`=x^2-4x+4-x^{2}+4x-3`$\\$`(x^{2}-x^{2})+(-4x+4x)+(-3+4)`$\\$`=1`

`2)`

`(x+3)^{2}-(x-3)^{2}-12`$\\$`=x^{2}+6x+9-(x^{2}-6x+9)-12`$\\$`=x^{2}+6x+9-x^{2}+6x-9-12`$\\$`=(x^{2}-x^{2})+(6x+6x)+(9-9-12)`$\\$`=12x-12`

`3)`

`3(x-y)^{2}-2(x+y)^{2}`

`=3(x^{2}-2xy+y^{2})-2(x^{2}+2xy+y^{2})`

`=3x^{2}-6xy+3y^{2}-2x^{2}-2xy-2y^{2}`

`=(3x^{2}-2x^{2})+(-6xy-2xy)+(3y^{2}-2y^{2})`

`=x^{2}-8xy+y^{2}`

`4)`

`(x+2)(x-2)-(3x+5)(3x-5)`

`=(x^{2}-2^{2})-[(3x)^{2}-5^{2}]`

`=x^{2}-4-9x^{2}+25`

`=(x^{2}-9x^{2})+(25-4)`

`=-8x^{2}+21`

`5)`

`(2x-1)(1+2x)+(x+2)^{2}`

`=[(2x)^{2}-1^{2}]+(x^{2}+4x+4)`

`=4x^{2}-1+x^{2}+4x+4`

`=(4x^{2}+x^{2})+4x+(-1+4)`

`=5x^{2}+4x+3`

`6)`

`6(x+1)(x-1)-(3x-2)^{2}`

`=6(x^{2}-1^{2})-[(3x)^{2}-2.3x.2+2^{2}]`

`=6(x^{2}-1)-(9x^{2}-12x+4)`

`=6x^{2}-6-9x^{2}+12x-4`

`=(6x^{2}-9x^{2})+12x+(-6-4)`

`=-3x^{2}+12x-10`

Áp dụng các hằng đẳng thức :

Số 1 : `(a+b)^{2}=a^{2}+2ab+b^{2}`

Số 2 : `(a-b)^{2}=a^{2}-2ab+b^{2}`

Số 3 : `a^{2}-b^{2}=(a-b)(a+b)`

`1) (x-2)^2-(x-3)(x-1)` 

`=x^2 - 2.2x + 2^2 - (x^2-x-3x+3)`

`= x^2-4x+4-x^2+4x-3`

`= (x^2-x^2)-(4x-4x) +(4-3)`

`= 1`

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`2) (x+3)^2-(x-3)^2-12`

`=(x+3-x+3)(x+3+x-3)-12`

`= 6.2x-12`

`=12x-12`

`=12(x-1)`

_____________________________

`3)  3(x-y)^2-2(x+y)^2`

`= 3(x^2-2xy+y^2)-2(x^2+2xy+y^2)`

`= 3x^2-6xy+3y^2-2x^2 - 4xy-2y^2`

`=(3x^2-2x^2)-(6xy+4xy)+(3y^2-2y^2)`

`= x^2 - 10xy + y^2`

_____________________________

`4) (x+2)(x-2)-(3x+5)(3x-5)`

`=x^2-4-[(3x)^2 -25]`

`=x^2-4-9x^2+25` 

`=(x^2-9x^2)+(-4+25)`

`= -8x^2+21` 

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`5) (2x-1)(1+2x)+(x+2)^2`

`= (2x-1)(2x+1)+x^2+2.2x+2^2`

`= (2x)^2-1+x^2+4x+4`

`= 4x^2+x^2+4x-1+4`

`= (4x^2+x^2)+4x+(-1+4)`

`= 5x^2+4x+3`

_____________________________

`6) 6(x+1)(x-1)-(3x-2)^2`

`= 6(x^2-1)-(9x^2-12x+4)`

`= 6x^2-6-9x^2+12x-4`

`=(6x^2-9x^2)+12x-(6+4)`

`= -3x^2+12x - 10`