Đáp án:a/ $(x - y)(x + y - 4xy)$
b/ (x - 3 - 2y)(x - 3 + 2y)
c/ (x - 2)(x - 5)
d/ (y + 2)(6x - 4)
e/ (x - 3 - y)(x - 3 + y)
g/ (x - 1)(x + 6)
2/ ${x^2} - 18x - 27$
Giải thích các bước giải:
a/$\eqalign{
& {x^2} - 4{x^2}y + 4x{y^2} - {y^2} \cr
& = ({x^2} - {y^2}) - (4{x^2}y - 4x{y^2}) \cr
& = (x - y)(x + y) - 4xy(x - y) \cr
& = (x - y)(x + y - 4xy) \cr} $
b/ ${x^2} - 6x + 9 - 4{y^2} = {(x - 3)^2} - {(2y)^2} = (x - 3 - 2y)(x - 3 + 2y)$
c/ ${x^2} - 7x + 10 = {x^2} - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 2)(x - 5)$
d/ $6xy + 12x - 4y - 8 = 6x(y + 2) - 4(y + 2) = (y + 2)(6x - 4)$
e/ ${x^2} - {y^2} - 6x + 9 = ({x^2} - 6x + 9) - {y^2} = {(x - 3)^2} - {y^2} = (x - 3 - y)(x - 3 + y)$
g/ ${x^2} + 5x - 6 = {x^2} - x + 6x - 6 = x(x - 1) + 6(x - 1) = (x - 1)(x + 6)$
2/ ${x^2}(1 - x) + (x + 3)({x^2} - 3x - 9) = {x^2} - {x^3} + {x^3} - 3{x^2} - 9x + 3{x^2} - 9x - 27 = {x^2} - 18x - 27$
