Question

[Phùng Đức Tài]

mọi ng giúp e

Answer 1

[Akai Haruma]

2.26:

a. $x^2-6x+9-y^2=(x^2-6x+9)-y^2=(x-3)^2-y^2$
$=(x-3-y)(x-3+y)$

b. $4x^2-y^2+4y-4=4x^2-(y^2-4y+4)$

$=(2x)^2-(y-2)^2=(2x-y+2)(2x+y-2)$
c. $xy+z^2+xz+yz=(xy+xz)+(z^2+yz)=x(y+z)+z(z+y)$
$=(y+z)(x+z)$
c.

$x^2-4xy+4y^2+xz-2yz$
$=(x^2-4xy+4y^2)+(xz-2yz)$
$=(x-2y)^2+z(x-2y)=(x-2y)(x-2y+z)$

Answer 2

[Akai Haruma]

2.27:

a. $x^3+y^3+x+y=(x^3+y^3)+(x+y)$
$=(x+y)(x^2-xy+y^2)+(x+y)=(x+y(x^2-xy+y^2+1)$
b. $x^3-y^3+x-y=(x^3-y^3)+(x-y)=(x-y)(x^2+xy+y^2)+(x-y)$

$=(x-y)(x^2+xy+y^2+1)$

c.

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

d.

$x^3-3x^2y+3xy^2-y^3+y^2-x^2$
$=(x^3-3x^2y+3xy^2-y^3)-(x^2-y^2)$
$=(x-y)^3-(x-y)(x+y)=(x-y)[(x-y)^2-(x+y)]$

$=(x-y)(x^2-2xy+y^2-x-y)$