e) Ta có: \(a^3-a^2-a+1\)

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

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

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

f) Ta có: \(x^3-2xy-x^2y+2y^2\)

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

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

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

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

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

d) Đề sai ko ???

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

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

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

\(b,=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)

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

\(d,=2\left(x^2+2xy+y^2-4z^2\right)=2\left(\left(x+y\right)^2-4z^2\right)=2\left(x+y-2z\right)\left(x+y+2z\right)\)

\(e,=a^2\left(a-1\right)-\left(a-1\right)=\left(a-1\right)\left(a^2-1\right)\)

\(f,=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x^2-2y\right)\left(x-y\right)\)

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 )

Vô đây xem: bài 1:phân tích đa thức thành nhân tửa)7x^3y-14x^2y+7xy^3b)3x^2-3xy-5x+5yc)x^2+7x+12giúp mình với  - Hoc24

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

\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)

\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)

\(\Leftrightarrow3\left(x-y\right)\)

d) \(3x^2-7x+4\)

\(\Leftrightarrow3x^2-7x+7-3\)

\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)

\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)

\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)

\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)

\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)

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

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

\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)

f) \(x^2+2xy+y^2-2x-2y\)

\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)

\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)

k) \(2x^2+5x+3\)

\(\Leftrightarrow2x^2+2x+3x+3\)

\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)

\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)

l) \(x^2-2x-y^2+1\)

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

\(\Leftrightarrow\left(x-1\right)^2-y^2\)

\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)

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

\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)

\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)

\(\Leftrightarrow3\left(x-y\right)\)

d) \(3x^2-7x+4\)

\(\Leftrightarrow3x^2-7x+7-3\)

\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)

\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)

\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)

\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)

\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)

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

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

\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)

f) \(x^2+2xy+y^2-2x-2y\)

\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)

\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)

k) \(2x^2+5x+3\)

\(\Leftrightarrow2x^2+2x+3x+3\)

\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)

\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)

l) \(x^2-2x-y^2+1\)

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

\(\Leftrightarrow\left(x-1\right)^2-y^2\)

\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)

\(a,=7xy\left(x^2-2xy+y^2\right)=7xy\left(x-y\right)^2\\ b,=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\\ c,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\)

1) \(\left(x+1\right)^2-16y^2\)

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

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

2) \(2x^2-8\)

\(=\left[\left(\sqrt{2x}\right)^2\right]^2-\left(\sqrt{8}\right)^2\)

\(=\left[\left(\sqrt{2x}\right)^2-\sqrt{8}\right].\left[\left(\sqrt{2x}\right)^2+\sqrt{8}\right]\)

6) \(x^2+1-y^2+2x\)

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

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

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

\(=\left(x+1-y\right).\left(x+1+y\right)\)

Chúc bạn học tốt!

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

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

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

5x^4-3x^3y+2xy^3-x^3y+2y^4-7x^2y-2x^3

= 5x^4+(3x^3y-x^3y)+2xy^3+2y^4-7x^2y-2x^3

=5x^4+2x^3y+2xy^3+2y^4-7x^2y-2x^3

\(5x^4-3x^3y+2xy^3-x^3y+2y^4-7x^2y^2-2x^3\)

\(=5x^4+\left(-3x^3y-x^3y\right)+2xy^3+2y^4-7x^2y^2-2x^3\)

\(=5x^4-4x^3y+2xy^3+2y^4-7x^2y^2-2x^3\)

e: \(49-x^2-2xy-y^2\)

\(=49-\left(x+y\right)^2\)

\(=\left(7-x-y\right)\left(7+x+y\right)\)

d: \(16x^2-24xy+9y^2=\left(4x-3y\right)^2\)

a)=xyz(x-x^2y^2+z)

e)=7²+(x-y)² 

^{[7+(y-x)].[(7-(y-x)] còn lại tự làm ;)}

b)=3x(x-2y+5y²z)

\(2x\left(x^2-7x-3\right)=2x^3-14x-6x\)

\(4xy^2\left(-2x^3+y^2-7xy\right)=-8x^4y^2+4xy^5-28x^2y^3\)

\(a,=x\left(x-2\right)^2\\ b,=\left(x-y\right)^2-9=\left(x-y-3\right)\left(x-y+3\right)\\ c,=x^2\left(2x-1\right)-4\left(2x-1\right)=\left(x-2\right)\left(x+2\right)\left(2x-1\right)\\ d,=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\\ e,=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\\ f,=x\left[\left(x-2\right)^2-y^2\right]=x\left(x-y-2\right)\left(x+y-2\right)\\ g,=x\left[\left(x-y\right)^2-25\right]=x\left(x-y-5\right)\left(x-y+5\right)\\ h,=x^3-x-2x+2=x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x-2\right)=\left(x-1\right)^2\left(x+2\right)\\ i,=3x^2+3x-10x-10=\left(x+1\right)\left(3x-10\right)\)