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7 tháng 11 2015

\(81x^2-6yz-9y^2-z^2=81x^2-\left(6yz+9y^2+z^2\right)\)

\(=81x^2-\left(9y^2+6xy+z^2\right)=81x^2-\left(3y+z\right)^2\)

\(=\left(9x-3y-z\right)\left(9x+3y+z\right)\)

29 tháng 6 2019

a) = x2 (y - x) - 9( y - x) = ( y - x ) ( x2 - 9) = ( y -x) ( x - 3 ) ( x + 3)

b) = x( x - 1 ) - 16 ( x - 1 ) = ( x - 1 ) ( x2 - 16 ) = ( x - 1 ) ( x - 4 ) ( x + 4 )

c) = (9x)2 - ( 9y2 + 6yz + z) = (9x)2 - ( 3y + z)2 = (9x - 3y - z ) ( 9x + 3y + z)

d) = z( x - y) - ( x2 -2xy + y2 ) = z(x - y) - (x - y)2 = (x - y) (z - 1)

e) = (x + 3) (x + 5)

f) = (x - 4) ( x + 3)

g) = (9x)2 + 2.9x.2 + 2- 36x = (9x + 2)2 - (\(6\sqrt{x}\))2 = \(\left(9x+2+6\sqrt{x}\right)\)\(\left(9x+2-6\sqrt{x}\right)\)

29 tháng 6 2019

a) x2y - x3 - 9y + 9x = x2(y - x) - 9(y - x) = (y - x)(x2 - 9) = (y - x)(x + 3)(x - 3).

b) x2(x - 1) + 16(1 - x) = (x - 1)(x2 - 16) = (x - 1)(x - 4)(x + 4).

c) 81x2 - 6yz - 9y2 - z2 = (9x)2 - ((3y)2 + 2.3yz + z2) = (9x)2 - (3y + z)2 = (9x + 3y +z)(9x - 3y - z).

d) xz - yz - x2 + 2xy - y2 = z(x - y) - (x - y)2 = (x - y)(z - x + y).

e) x2 + 8x + 15 = (x2 + 3x) + (5x + 15) = x(x + 3) + 5(x + 3) = (x + 3)(x + 5).

f) x2 - x - 12 = (x2 - 4x) + (3x - 12) = x(x - 4) + 3(x - 4) = (x - 4)(x + 3).

g) (Đề sai) 81x4 + 4 = (81x4 + 36x2 + 4) - 36x2 = (9x2 + 2)2 - 36x2 = (9x2 + 2 + 6x)(9x2 + 2 - 6x).

25 tháng 5 2017

a)\(81x^2-6yz-9y^2-z^2\)

\(=81x^2-\left(z-3y\right)^2\)

\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)

b)\(x^2y-x^3-9y+9x\)

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

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

c)\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4z^2\right)\)

\(=3\left[\left(a-b\right)^2-4z^2\right]\)

\(=3\left(a-b-2z\right)\left(a-b+2z\right)\)

26 tháng 5 2017

a)\(81x^2-6yz-9y^2-z^2=\left(9x\right)^2-\left(9y^2+6yz+z^2\right)=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x-3y-z\right)\left(9x+3y+z\right)\)b)\(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)

c)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

21 tháng 6 2015

a. x4+2= (x4+\(2\sqrt{2}x^2+2\)) - \(2\sqrt{2}x^2^{ }\) = 

\(\left(x^2+\sqrt{2}\right)^2-2\sqrt{2}x^2=\left(x^2-\sqrt{2\sqrt{2}}x+\sqrt{2}\right)\left(x^2+2\sqrt{2}x+\sqrt{2}\right)\)b. 81x2-(9y2+6yz+z2)=81x2 - (3y+z)2=(9x-3y-z)(9x+3y+z)

14 tháng 10 2017

a. 6x3y2 ( 2-x) + 9x2y2 (x-2)

= -6x3y2 (x-2) + 9x2y( x-2)

= (x-2) 3x2y2 ( -2x + 3)

b. x2 - 4x + 4y - y

= x- y2 - (4x - 4y )

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

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

c. 81x+ 6yz -9y2-z2 

= 81x - (9y2 - 6yz + z2 )

= (9x)2 - ( 3y - z )2

= (9x + 3y -z)(9x - 3y + z )

14 tháng 10 2017

\(a,=6x^3y^2\left(2-x\right)-9x^2y^2\left(2-x\right)\)

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

\(f,=\left(x-3-x-2\right)\left(x-3+x+2\right)\)

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

\(g,=\left(x-3\right)\left(x+3\right)+2\left(x+3\right)\)

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

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

2 tháng 8 2017

a)

\(4x^2-9y^2+6x-9y=\left(2x-3y\right)\left(2x+3\right)+3\left(2x-3y\right)\)

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

b)

\(1-2x+2yz+x^2-y^2-z^2=\left(x^2-2x+1\right)-\left(y^2-2yz+z^2\right)\) (đổi dấu)

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

c)

\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5\left(x+1\right)+3\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)

\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)

2 tháng 8 2017

(2x-3y)(2x+3y) chớ x + 3 k ik

1 tháng 11 2019

A.5X2+3(X+Y)2-5Y2

= 5.(x2 - y2) + 3(x+y)2

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

= ( x+y).[(5.( x-y) + 3(x+y)]

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

=( x+y).( 8x - 2y)

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

C.81x2 - 6yz - 9y2 - z2

=( 9x)2 - (z2 + 6yz+ 9y2)

=( 9x)2 -( z +3y)2

=(9x - z -3y).(9x + z+3y)

D.x2y-x3-9y+9x

=9.(x - y) + x2(y - x)

= 9.(x-y) - x2(x-y)

=(x+y).[32- x2]

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

E.x3+9x2-4x-36

=(x3-4x) + (-36 +9x2)

=x.(x2-4) + 9.(x2-4)

=(x2-4).(x+9)

H.2x3+x2-8x-4

= x2.(2x+1)-4.(2x +1)

=(2x +1).(x2 -4)

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

Cậu xem trước nhé

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

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

\(B=a^2+b^2-a^2b^2+ab-a-b=\left(ab-a\right)-\left(a^2b^2-a^2\right)+\left(b^2-b\right)\)

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

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

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

1 tháng 8 2016

Đoàn Thị Huyền Đoan: Hình như câu A bạn chép xuống bị sai đề rồi!

13 tháng 9 2017

a)\(x^2-6xy+9y^2-25z^2=\left[x^2-2.x.3y+\left(3y\right)^2\right]-\left(5z\right)^2\)

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

b)\(xyz+x^2yz-6yz=yz\left(x^2+x-6\right)=yz\left(x^2+3x-2x-6\right)\)

\(=yz\left[x\left(x+3\right)-2\left(x+3\right)\right]=yz\left(x-2\right)\left(x+3\right)\)

13 tháng 9 2017

a.x2-6xy+9y2​-25z​2

​= ( x​2-6xy+9y2)-25z2

​= [x​2-2x3y+(3y)2]-25z2

​= (x-3y)2-252

​= (x-3y+25)(x-3y-25)