a)x^2-(a+b)x+ab

= x^2 - ax - bx + ab

= (x^2 - ax) - (bx - ab)

= x(x-a) - b(x-a)

= (x-b)(x-a) 

b)7x^3-3xyz-21x^2+9z

= 

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

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

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

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

d) y^2+y-x^2+x

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

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

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

e)4x^2-2x-y^2-y

= [(2x)^2 - y^2] - (2x +y)

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

= (2x -y -1)(2x+y)

f)9x^2-25y^2-6x+10y

= 

ko biết làm

a: =3x(y-2)-5(y-2)

=(y-2)(3x-5)

b: =(2x-5y)(2x+5y)

c: =x(x^3-8)

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

a)

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

b)

\(4x^2-25y^2\\ =\left(2x-5y\right)\left(2x+5y\right)\)

c)

\(x^4-8x\\ =x\left(x^3-8\right)\\ =x\left(x-2\right)\left(x^2+2x+4\right)\)

\(a,3x\left(y-2\right)+5\left(2-y\right)=3x\left(y-2\right)-5\left(y-2\right)=\left(y-2\right)\left(3x-5\right)\)

\(b,4x^2-25y^2=\left(2x-5y\right)\left(2x+5y\right)\)

\(c,x^4-8x=x\left(x^3-8\right)=x\left(x-2\right)\left(x^2+4x+4\right)\)

Phân tích các đa thức sau thành nhân tử ... c) 6x(x+y)^2+3x^2y(x+y). 2: .... x³ - 5x + 8x - 4=x² . x -5x + 8x -2² = (x² - 2²) . (x -5x + 8x )=(x-2) . (x+2) . 4x. x³ - 9x² ..... Phân tích các đa thức sau thành nhân tử : a,x^3+5x^2+8x+4 b, x^3-9x^2+6x+16 .

\(a.=x^2\left(x-y\right)-25\left(x-y\right)\)

\(=\left(x-5\right)\left(x+5\right)\left(x-y\right)\)

\(b.=\left(b-a\right)\left(b+a\right)-4\left(b-a\right)\)

\(=\left(b+a-4\right)\left(b-a\right)\)

a ) x³ - x²y - 25x + 25y

= x² . ( x - y ) - 25 . ( x - y )

= ( x - y )( x² - 25 )

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

b ) b² - 4b + 4a - a²

= ( b² - a² ) - ( 4b - 4a )

= ( b - a )( a + b ) - 4 . ( b - a )

= ( b - a )( a + b - 4 )

c ) x³ - 4x² - 8x + 8

= ( x³ + 8 ) - ( 4x² + 8x )

= ( x + 2 )( x² - 2x + 4 ) - 4x . ( x + 2 )

= ( x + 2 )( x² - 2x + 4 - 4x )

= ( x + 2 )( x² - 6x + 4 )

a,\(x^2+4x-25y^2+4=\left(x^2+4x+4\right)-\left(5y\right)^2=\left(x+2\right)^2-\left(5y\right)^2\)

                                         \(=\left(x+2-5y\right)\left(x+2+5y\right)\)

b, \(x^3-4x^2-8x+8=\left(x^3+8\right)-\left(4x^2+8x\right)\)

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

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

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

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

Mk làm sai câu b nha , phảo làm như sau 

\(x^3-4x^2-8x+8=\left(x^3+8\right)-\left(4x^2+8x\right)\)

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

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

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

a

\(xy+3x-7y-21\\ =\left(xy+3x\right)-\left(7y+21\right)\\ =x\left(y+3\right)-7\left(y+3\right)\\ =\left(y+3\right)\left(x-7\right)\)

b

\(2xy-15-6x+5y\\ =\left(2xy-6x\right)-\left(15-5y\right)\\ =2x\left(y-3\right)-5\left(3-y\right)\\ =2x\left(y-3\right)+5\left(y-3\right)\\ =\left(y-3\right)\left(2x+5\right)\)

c Đề phải là \(\left(2x^2y+2xy^2-x-y\right)\) mới phân tích được: )

\(=2xy\left(x+y\right)-\left(x+y\right)\\ =\left(x+y\right)\left(2xy-1\right)\)

d

\(7x^3y-3xyz-21x^2+9z\\ =\left(7x^3y-21x^2\right)-\left(3xyz-9z\right)\\ =7x^2\left(xy-3\right)-3z\left(xy-3\right)\\ =\left(xy-3\right)\left(7x^2-3z\right)\)

e

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

f

\(9x^2-25y^2-6x+10y\\ =\left(3x\right)^2-\left(5y\right)^2-\left(6x-10y\right)\\ =\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\\ =\left(3x-5y\right)\left(3x+5y-2\right)\)

a: =x(y+3)-7(y+3)

=(y+3)(x-7)

b: \(=2xy-6x+5y-15\)

=2x(y-3)+5(y-3)

=(y-3)(2x+5)

c: \(=2xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(2xy-1\right)\)

d: \(=xy\left(7x^2-3z\right)-3\left(7x^2-3z\right)\)

=(7x^2-3z)(xy-3)

e: =4x^2-y^2-2x-y

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

=(2x+y)(2x-y-1)

f: =(3x-5y)(3x+5y)-2(3x-5y)

=(3x-5y)(3x+5y-2)

1) \(3x\left(x-1\right)+5\left(x-1\right)\)

\(=\left(x-1\right)\left(3x+5\right)\)

2) \(4x(x-2y)-8y(2y-x)\)

\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)

\(=\left(4x+8y\right)\left(x-2y\right)\)

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

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

\(=a^2\left(x-1\right)-b^2\left(x-1\right)\)

\(=\left(a^2-b^2\right)\left(x-1\right)\)

\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)

4) \(3x\left(x-a\right)+4a\left(a-x\right)\)

\(=3x\left(x-a\right)-4a\left(x-a\right)\)

\(=\left(x-a\right)\left(3x-4a\right)\)

5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)

\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)

\(=\left(5x+10y^2\right)\left(x-y\right)^2\)

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

6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)

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

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

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

7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)

\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)

\(=\left(x-y\right)\left(a-m\right)^2\)

8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)

\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)

\(=\left(6y^2+9x\right)\left(x-1\right)^2\)

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

#Ayumu

i. Ta có: (x+y)^3 - (x-y)^3=[(x+y)-(x-y)][(x+y)^2 + (x+y)(x-y) + (x-y)^2]

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

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

có hằng đẳng thức (x+y)^3 vs (x-y)^3 thì sao bạn phải làm như vậy nữa

bạn xem mình làm như này có đúng không:

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

= 2 . 3x^2y = 6x^2y

\(a,=x\left(x+5\right)\\ b,=\left(y-1\right)^2-4x^2=\left(y-1-2x\right)\left(y-1+2x\right)\\ c,\text{Không phân tích đc}\)

a) \(x^{2}+5x=x(x+5)\)

b)\(y^{2}-4x^{2}-2y+1 = (y-1)^{2}-4x^{2}=(y-1-2x)(y-1+2x)\)

c)\(x^{2}-8x+16=(x-4)^{2}\)

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

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

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

c x^2(x+1)-4(x+1)

(x+1).(x^2-4)

d x^4-(x^2-2x+1)

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

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

MIK KO BIT DUNG HAY KO CON B THI MIK KO BIET LAM

Câu b dễ thôi

\(x^4-4x^3-8x^2+8x\)

\(=x\left(x^3-4x^2-8x+8\right)\)

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