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

b,2(xy+xyz-2x-2z)

c, 3(x^2-xy-x-y)

a) Ta có : 2x² - 4x + 2xy - 4y 

= 2x(x - 2) + 2y(x - 2) 

= (x - 2)(2x + 2y) 

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

a) 5xy² . (-3y)²

= 5xy² . 9y²

= (5.9).x.(y².y²)

= 45xy⁴

Hệ số: 45

Bậc: 5

b) x²yz . (-2xy)³

= x²yz . (-8x³y³)

= -8.(x².x³).(y.y³).z

= -8x⁵y⁴z

Hệ số: -8

Bậc: 10

c) (-2x²y)².8x³yz³

= 4x⁴y².8x³yz³

= (4.8).(x⁴.x³).(y².y).z³

= 32x⁷y³z³

Hệ số: 32

Bậc: 13

d) (-2xy³)².(-2xyz)³

= 4x²y⁶.(-8x³y³z³)

= [4.(-8)].(x².x³).(y⁶.y³).z³

= -32x⁵y⁹z³

Hệ số: -32

Bậc: 17

e) (-5xy³z).(-4x²)²

= (-5xy³z).(16x⁴)

= (-5.16).(x.x⁴).y³.z

= -80x⁵y³z

Hệ số: -80

Bậc: 9

f) (2x²y³)².(-2xy)

= (4x⁴y⁶).(-2xy)

= [4.(-2)].(x⁴.x).(y⁶.y)

= -8x⁵y⁷

Hệ số: -8

Bậc: 12

a: =5xy^2*9y^2=45xy^4

b: =x^2yz*(-8)x^3y^3=-8x^5y^4z

c: =4x^4y^2*8x^3yz^3=32x^7y^3z^3

d: =4x^2y^6*(-8)x^3y^3z^3=-32x^5y^9z^3

e: =-5xy^3z*16x^4=-80x^5y^3z

f: =4x^4y^6*(-2xy)=-8x^5y^7

Bài 1:

a: \(7xy^2\left(9xy^4+2xy+1\right)\)

\(=7xy^2\cdot9xy^4+7xy^2\cdot2xy+7xy^2\cdot1\)

\(=63x^2y^6+14x^2y^3+7xy^2\)

b: \(\frac12xyz\left(6x^2y^3+4x^3y-3xy\right)\)

\(=\frac12xyz\cdot6x^2y^3+\frac12xyz\cdot4x^3y-\frac12xyz\cdot3xy\)

\(=3x^3y^4z+2x^4y^2z-\frac32x^2y^2z\)

Bài 2:

1: \(5x^2y+10xy^3=5xy\cdot x+5xy\cdot2y^2=5xy\left(x+2y^2\right)\)

2: \(15xy^4-9xy=3xy\cdot5y^3-3xy\cdot3=3xy\left(5y^3-3\right)\)

3: \(5x^2+10xy+5y^2=5\left(x^2+2xy+y^2\right)=5\left(x+y\right)^2\)

Để tính các biểu thức trên, ta sẽ áp dụng quy tắc nhân đa thức.

a) 2xy(3x+1) = 6x^2y + 2xy

b) -6x^2y(4x-5) = -24x^3y + 30x^2y

c) -3x^2(4x^2y-6xy) = -12x^4y + 18x^3y

d) 1/2xy^2(2x+3) = xy^2 + 3/2xy^2

e) 8x^2y^2(1/4xy-1/2x^2) = 2xy - 4x^2y^2

f) 5x(x^2+3x+1) = 5x^3 + 15x^2 + 5x

g) -1/2x^2y(2xy+6) = -x^3y - 3x^2y

1/x^3 - 2x^2 - 9x + 18

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

2/3x^2 -5x - 3y^2 + 5y

= 3( x\(^2\) - y\(^2\) ) - 5 ( x - y ) = 3 ( x - y ) ( x + y ) - 5 ( x - y ) = ( x - y ) [ 3( x+ y ) - 5 ]

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

3/49 - x^2 + 2xy - y^2

= 49 - ( x\(^2\) - 2xy + y\(^2\) ) = 49 - ( x - y )\(^2\) = ( 7 - x + y ) ( 7 + x - y )

5/ x^2 - 4x^2y^2 + 2xy

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

6/ 3x - 3y - x^2 + 2xy - y^2

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

\(a,3x\left(3x+6\right)=9x^2+18x\)

\(b,-\dfrac{1}{2}xy\left(4x^2+6x\right)\)

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

\(c,-2x^2y^3\left(\dfrac{1}{2}xy+4y^2\right)\)

\(=-x^3y^4-8x^2y^5\)

\(d,-6x^2\left(\dfrac{1}{3}xy^2-\dfrac{1}{2}y\right)\)

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

#\(Urushi\)

a) 3x(3x+6) = 9x^2 + 18x b) -1/2xy(4x^2+6x) = -2x^3y - 3xy c) -2x^2y^3(1/2xy+4y^2 ) = -x^2y^2 - 8x^2y^5 d) -6x^2(1/3xy^2-1/2y) = -2xy + 3x^2y

Vậy kết quả của các biểu thức là: a) 9x^2 + 18x b) -2x^3y - 3xy c) -x^2y^2 - 8x^2y^5 d) -2xy + 3x^2y

a)\(\left(3x+2\right)\left(2x-3\right)=6x^2-5x-6\)

b) viết lại đề nhin (dùng f(x) viết mới rõ ra dduocj) ko phải dùng {[(...)]} cho chuẩn vào

c) \(\left(x-2\right)^3-x^2.\left(x-6\right)=x^3-3.x.2\left(x-2\right)-8-x^3+6x^2\)

\(=x^3-6x^2+12x-8-x^3+6x^2=12x-8=4\Rightarrow x=1\)

a) ( x - 1 )³ + 3x( x - 1 )² + 3x²( x - 1 ) + x³

= [ ( x - 1 ) + x ) ]³ ( HĐT số 4 )

= [ x - 1 + x ]³

= [ 2x - 1 ]³ 

=> đpcm

b) ( x² - 2xy )³ + 3( x² - 2xy )y² + 3( x² - 2xy )y⁴ + y⁶

= [ ( x² - 2xy ) + y² ]³ ( HĐT số 4 )

= [ x² - 2xy + y² ]³

= [ ( x - y )² ]³

= ( x - y )⁶

=> đpcm