Đáp án+Giải thích các bước giải:
`1)` Cách 1: `(x^2+x)^2+4x^2+4x-12`
`=x^4+2x^3+4x^2+4x-12`
`=x^4+x^3+x^3+6x^2-2x^2+6x-2x-12`
`=(x^4+x^3-2x^2)+(x^3+x^2-2x)+(6x^2+6x-2)`
`=x^2(x^2+x-2)+x(x^2+x-2)+6(x^2+x-2)`
`=(x^2+x+6)(x^2+x-2)`
`=(x-1)(x+2)(x^2+x+6)`
Cách 2:`(x^2+x)+4x^2+4x-12`
`=(x^2+x)+4(x^2+x)+4-16`
`=(x^2+x+2)^2-4^2`
`=(x^2+x+6)(x^2+x-2)`
`=(x^2+x+6)(x-1)(x+2)`
`2) x^2+2xy+y^2+2x+2y-15`
`=(x+y)^2+2(x+y)+1-16`
`=(x+y+1)^2-4^2`
`=(x+y+5)(x+y-3)`
`3) (x^2+x)^2+3(x^2+x)+2`
`= (x^2+x)^2+2 . 3/2.(x^2+x)+(3/2)^2-1/4`
`=(x^2+x+3/2)^2-(1/2)^2`
`=(x^2+x+2)(x^2+x+1)`
`4) x^2-2xy+y^2+3x-3y-10`
`=(x-y)^2+3(x-y)+9/4-(49)/4`
`=(x-y+9/4)^2-(7/2)^2`
`=(x-y+(23)/4)(x-y-5/4)`
`5)` `x^2-4xy+4y^2-2x+4y-35`
`=x^2-2xy-2xy+4y^2-7x+5x+14y-10y-35`
`=(4y^2-2xy+14y)-(2xy-x^2+7x)-(10y-5x+35)`
`=2y(2y-x+7)-x(2y-x+7)-5(2y-x+7)`
`=(2y-x-5)(2y-x+7)`
