a) \(a\left(x-y\right)+bx-by\)

\(=a\left(x-y\right)+b\left(x-y\right)\)

\(=\left(a-b\right)\left(x-y\right)\)

\(a,a\left(x-y\right)+bx-by\)

\(=a\left(x-y\right)+b\left(x-y\right)\)

\(=\left(a+b\right)\left(x-y\right)\)

\(b,ac+bc+a+b\)

\(=\left(a+b\right)c+\left(a+b\right)\)

\(\left(a+b\right)\left(c+1\right)\)

\(c,5x^2-5ax-7a+7x\)

\(=5x\left(x-a\right)-7\left(a-x\right)\)

\(=5x\left(x-a\right)+7\left(x-a\right)\)

\(=\left(5x+7\right)\left(x-a\right)\)

\(d,7z^2-7yz-4z+4y\)

\(=7z\left(z-y\right)-4\left(z-y\right)\)

\(=\left(7z-4\right)\left(z-y\right)\)

\(e,x^3+3x^2+3x+9\)

\(=\left(x^3+3x^2\right)+\left(3x+9\right)\)

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

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

\(f,x^3-x^2y-x^2z-xyz\)

\(=\left(x^3-x^2y\right)+\left(-x^2z-xyz\right)\)

\(=x^2\left(x-y\right)-xz\left(x-y\right)\)

\(=\left(x^2-xz\right)\left(x-y\right)\)

\(=x\left(x-z\right)\left(x-y\right)\)

\(g,pq-p^2-5\left(p-q\right)\)

\(=\left(pq-p^2\right)-5\left(p-q\right)\)

\(=p\left(q-p\right)+5\left(q-p\right)\)

\(=\left(p+5\right)\left(q-p\right)\)

a) (x³-x²)+(8x-8)=x(x-1)+8(x-1)=(x²+8)(x-1)

b) 8x³-8x²y+2xy²=2x(4x²-4xy+y²)

c) (x²+y²-z²)² - 4x²y²=(x²+y²-z²)² - (2xy)²=(x²+y²-z²-2xy)(x²+y²-z²+2xy)

`a, P = 2x(3 - x^2)`

`b, Q = 5x^2(x-3y)`

`c, R = xy(3x^2y^2 - 6y^2z + 1)`

a) \(P=6x-2x^3\)

\(P=2x\left(3+x^2\right)\)

b) \(Q=5x^3-15x^2y\)

\(Q=5x^2\left(x-3y\right)\)

c) \(R=3x^3y^3-6xy^3z+xy\)

\(R=xy\left(3x^2y^2-6y^2z+1\right)\)

a, \(=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)

b, \(\left(x+y-x+y\right)[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2]\)

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

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

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

câu a, b áp dụng hằng đẳng thức rồi làm nha 

c) 3x⁴y² + 3x³y² + 3xy² + 3y²

= ( 3x⁴y² + 3x³y² ) + ( 3xy² + 3y² )

= 3x³y² ( x + 1) + 3y² ( x + 1 )

= ( 3x³y² + 3y² ) ( x + 1 )

= 3y² ( x³ + 1 ) ( x + 1 )

= 3y² ( x + 1 ) ( x² - x + 1 ) ( x + 1 )

= 3y² ( x + 1 )² ( x² - x + 1 )

a) (xy +1)²- (x-y)²

=(xy +1-x+y)(xy+1+x-y)

b) (x + y)³ - (x - y)³

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

= 2y(x²+2xy+y²+x²+xy-xy-y²+x²-2xy+y²)

=2y(3x²+y²)

c) 3x⁴y² + 3x³y² + 3xy² + 3y²

=3y²(x⁴+x³+x+1)

= 3y²(x³(x+1)+(x+1)

= 3y²(x+1)(x³+1)

ko bt đúng ko

`b)x^3+y^3+z^3-3xyz`

`=x^3+3xy(x+y)+z^3-3xy(x+y)-3xyz`

`=(x+y)^3+z^3-3xy(x+y+z)`

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

`=(x+y+z)(x^2+2xy+y^2-zx-yz-3xy+z^2)`

`=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)`

giúp mk vs mk cần gấp T^T

Bạn xem lại đề câu b) nhé đề đúng là `x^3+y^3+z^3-3xyz`.Còn được thì xem lại câu c) nhé do số quá xấu.

`a)x^4+3x^3-6x^2-8`

`=x(x^3+3x^2-6x-8)`

`=x[(x-2)(x^2+2x+4)+3x(x-2)]`

`=x(x-2)(x^2+5x+4)`

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

`=x(x-2)(x+1)(x+4)`

`c)(x+1)(x+3)(x+5)(x+7)-5`

`=[(x+1)(x+7)][(x+3)(x+5)]-5`

`=(x^2+8x+7)(x^2+8x+15)-5`

`=(x^2+8x+11)^2-4^2-5`

`=(x^2+8x+11)^2-21`

`=(x^2+8x+11-sqrt21)(x^2+8x+11+sqrt21)`

a.

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

\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)

\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)

b.

\(=\left(x-y\right)^2-z\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y-z\right)\)

c.

\(=x^4-1+4x^2-4\)

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

\(=\left(x^2-1\right)\left(x^2+5\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

a) Ta có: \(x^3+3x^2+3x+1-27z^3\)

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

\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)

b) Ta có: \(x^2-2xy+y^2-zx+yz\)

\(=\left(x-y\right)^2-z\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y-z\right)\)

c) Ta có: \(x^4+4x^2-5\)

\(=x^4+4x^2+4-9\)

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

\(=\left(x^2-1\right)\left(x^2+5\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

` = -3(x-y)^2`

`c, (x+y)^2 - 2(x+y)z + z^2`

`= (x+y-z)^2`

a) $x^3-3x^2y+4x-12y$

$=(x^3-3x^2y)+(4x-12y)$

$=x^2(x-3y)+4(x-3y)$

$=(x-3y)(x^2+4)$

b) $4x^2-y^2+4y-4$

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

$=(2x)^2-(y^2-2\cdot y\cdot2+2^2)$

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

$=[2x-(y-2)][2x+(y-2)]$

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

c) $9x^2-6x-y^2+2y$

$=(9x^2-y^2)-(6x-2y)$

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

$=(3x-y)(3x+y)-2(3x-y)$

$=(3x-y)(3x+y-2)$

$\text{#}Toru$

bạn ấn ở chỗ x² cho rõ hơn nhé

\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)

c: =(x-5)(x+3)

e: =(x+1-y)(x+1+y)