Đáp án+ Giải thích các bước giải:
CT: $(A±B)^2=A^2±2AB+B^2$
$A^2-B^2=(A-B)(A+B)$
$(A±B)^3=A^3±3A^2B+3AB^2±B^3$
$A^3-B^3=(A-B)(A^2+AB+B^2)$
$a)x^2-3xy+x-3y=x(x-3y)+(x-3y)$
$=(x-3y)(x+1)$
$b)7x^2-7xy-4x+4y=7x(x-y)-4(x-y)$
$=(x-y)(7x-4)$
$c)x^2+6x-y^2+9= (x^2+6x+9)-y^2$
$=(x+3)^2-y^2=(x+3-y)(x+3+y)$
$d)x^2+y^2+x^2-9t^2-2xy+6zt$
$=(x^2-2xy+y^2)-(z^2-6zt+9t^2)$
$=(x-y)^2-(z-3t)^2$
$=(x-y-z+3t)(x-y+z-3t)$
$e)x^4+3x^3-9x-27=x^3(x+3)-9(x+3)$
$=(x+3)(x^3-9)$
$f)x^4+3x^3-9x-9=x^4-9+3x^3-9x$
$=(x^2-3)(x^2+3)+3x(x^2-3)$
$=(x^2-3)(x^2+3+3x)$
$g)x^3-3x^2+3x-1-8y^3=(x^3-3x^2+3x-1)-8y^3$
$=(x-1)^3-(2y)^3=(x-1-2y)[(x-1)^2+2y(x-1)+4y^2]$
$=(x-2y-1)(x^2-2x+1+2xy-2y+4y^2)$
$h)5x^2+10xy+5y^2=5(x^2+2xy+y^2)$
$=5(x+y)^2$
