Câu 1:

$x^2+4y^2+4xy-16=[x^2+(2y)^2+2.x.2y]-16$

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

Câu 2:

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

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

Câu 1:

\(x^2+4y^2+4xy-16\)

\(=\left(x+2y\right)^2-16\)

\(=\left(x+2y+4\right)\left(x+2y-4\right)\)

Câu 2:

\(x^3+x^2+y^3+xy\)

\(=\left(x^3+y^3\right)\left(x^2+xy\right)\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)+x\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-xy+y^2+x\right)\)

C1:x^2+4y^2+4xy-16

=[x^2+4xy+(2y)^2]-16

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

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

C2: x^3+x^2+y^3+xy

=(x^2+xy)+(x^3+y^3)

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

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

bài này ra lâu r nhưng ngứa tay nên giải luôn=)))))

\(a,x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right).\left(x-y+z\right)\)

\(b,x^3+y^3+2x^2-2xy+2y^2=\left(x^3+y^3\right)+2\left(x^2-xy+y^2\right)=\left(x+y\right).\left(x^2-2xy+y^2\right)+2.\left(x^2-xy+y^2\right)=\left(x^2-xy+y^2\right).\left(x+y+2\right)\)

a) (x - y)(x + y + 3).                    b) (x + y - 2xy)(2 + y + 2xy).

c) x 2 (x + l)( x 3  -  x 2  + 2).              d) (x – 1 - y)[ ( x   -   1 ) 2   +   ( x   -   1 ) y   +   y 2 ].

\(Sửa:x^3+y^3+2x^2+2xy\\ =\left(x+y\right)\left(x^2-xy+y^2\right)+2x\left(x+y\right)\\ =\left(x+y\right)\left(x^2-xy+y^2+2x\right)\)

\(=x\left(x^2-1\right)+3\left(x^2-1\right)=\left(x+3\right)\left(x^2-1\right)=\left(x+3\right)\left(x-1\right)\left(x+1\right)\)

a.

\(x^3-y^3+2x^2-2y^2\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x-y\right)\left(2x+2y\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)

b.

\(x^3+1-x^2-x\)

\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)

\(=x^3+2+3x^3-6=4x^3-4=4\left(x^3-1\right)=4\left(x-1\right)\left(x^2+x+1\right)\)

= x(x^2 + 2xy + y^2 - 25z^2)

= x(x + y - 5z)(x + y + 5z)

a) x⁴ + 2x² + 1

= (x²)² + 2.x².1 + 1²

= (x² + 1)²

b) 4x² - 12xy + 9y²

= (2x)² - 2.2x.3y + (3y)²

= (2x - 3y)²

c) -x² - 2xy - y²

= -(x² + 2xy + y²)

= -(x + y)²

d) (x + y)² - 2(x + y) + 1

= (x + y)² - 2.(x + y).1 + 1²

= (x - y + 1)²

e) x³ - 3x² + 3x - 1

= x³ - 3.x².1 + 3.x.1² - 1³

= (x - 1)³

g) x³ + 6x² + 12x + 8

= x³ + 3.x².2 + 3.x.2² + 2³

= (x + 2)³

h) x³ + 1 - x² - x

= (x³ + 1) - (x² + x)

= (x + 1)(x² - x + 1) - x(x + 1)

= (x + 1)(x² - x + 1 - x)

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

k) (x + y)³ - x³ - y³

= (x + y)³ - (x³ + y³)

= (x + y)³ - (x + y)(x² - xy + y²)

= (x + y)[(x + y)² - x² + xy - y²]

= (x + y)(x² + 2xy + y² - x² + xy - y²)

= (x + y).3xy

= 3xy(x + y)