Đáp án `+` Giải thích các bước giải:

`7, (x+y)^2 - 8(x+y) + 12`

`= (x + y)^2 - 2 . 4(x + y) + 16 - 4`

`= (x + y)^2 - 2 . 4 . (x + y) + 4^2 - 2^2`

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

`= (x + y - 4 - 2)(x + y - 4 + 2)`

`= (x + y - 6)(x + y - 2)`

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`8, (x^2 + 2x)^2 - 2x^2 - 4x - 3`

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

Đặt `x^2 + 2x = t ,` ta có:

`= t^2 - 2t - 3`

`= t^2 - 3t + t - 3`

`= t(t - 3) + 1(t - 3)`

`= (t + 1)(t - 3)`

Thay `x^2 + 2x = t` vào , ta đc:

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

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

`= (x +1)^2[x(x + 3) - 1(x + 3)]`

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

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`9, (x^2 + x)^2 + 4x^2 + 4x - 12`

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

`= (x^2 + x)^2 + 2 . 2(x^2 + x) + 4 - 16`

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

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

`= (x^2 + x - 2)(x^2 + x + 6)`

`= (x^2 - x + 2x - 2)(x^2 + x + 6)`

`= [x(x - 1) + 2(x - 1)](x^2 + x + 6)`

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

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`10, (x^2 + 2x)^2 + 9x^2 + 18x + 20`

`= (x^2 + 2x)^2 + 9(x^2 + 2x) + 20`

`= (x^2 + 2x)^2 + 5(x^2 + 2x) + 4(x^2 + 2x) + 20`

`= (x^2 + 2x)(x^2 + 2x + 5) + 4(x^2 + 2x + 5)`

`= (x^2 + 2x + 4)(x^2 + 2x + 5)`

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`11, (x^2 + x)^2 - 2(x^2 + x) - 15`

`= (x^2 + x)^2 - 2(x^2 + x) + 1 - 16`

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

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

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

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`12, (x^2 + 4x)^2 - 2(x^2 + 4x) - 15`

`= (x^2 + 4x)^2 - 2(x^2 + 4x) + 1 - 16`

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

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

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

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

`= [x(x - 1) + 5(x - 1)][x(x + 3) + 1(x + 3)]`

`= (x + 5)(x - 1)(x + 1)(x + 3)`