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A = xy + y - 2x - 2
= y( x + 1 ) - 2( x + 1 )
= ( x + 1 )( y - 2 )
B = x2 - 3x + xy - 3y
= x( x - 3 ) + y( x - 3 )
= ( x - 3 )( x + y )
C = 3x2 - 3xy - 5x + 5y
= 3x( x - y ) - 5( x - y )
= ( x - y )( 3x - 5 )
D = xy + 1 + x + y
= y( x + 1 ) + ( x + 1 )
= ( x + 1 )( y + 1 )
E = ax - bx + ab - x2
= ( ax - x2 ) + ( ab - bx )
= x( a - x ) + b( a - x )
= ( a - x )( x + b )
F = x2 + ab + ax + bx
= ( ax + x2 ) + ( ab + bx )
= x( a + x ) + b( a + x )
= ( a + x )( x + b )
G = a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
Bonus : = ( a - x )[ a2 - ( √y )2 ]
= ( a - x )( a - √y )( a + √y )
H = 2xy + 3z + 6y + xz
= ( 6y + 2xy ) + ( 3z + xz )
= 2y( 3 + x ) + z( 3 + x )
= ( 3 + x )( 2y + z )
A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1
B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)
C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)
D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)
E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)
F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)
G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)
a) \(x^3-2x^2+2x-1^3\)
\(=x\left(x^2-2x+1\right)+x-1\)
\(=x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\)
b) \(x^2y+xy+x+1\)
\(=xy\left(x+1\right)+\left(x+1\right)\)
\(=\left(xy+1\right)\left(x+1\right)\)
c) \(ax+by+ay+bx\)
\(=a\left(x+y\right)+b\left(x+y\right)\)
\(=\left(a+b\right)\left(x+y\right)\)
d) \(x^2-\left(a+b\right)x+ab\)
\(=x^2-ax-bx+ab\)
\(=\left(x^2-ax\right)-\left(bx-ab\right)\)
\(=x\left(x-a\right)-b\left(x-a\right)\)
\(=\left(x-b\right)\left(x-a\right)\)
e) Ko biết làm
f) \(ax^2+ay-bx^2-by\)
\(=\left(ax^2+ay\right)-\left(bx^2+by\right)\)
\(=a\left(x^2+y\right)-b\left(x^2+y\right)\)
\(=\left(a-b\right)\left(x^2+y\right)\)
1, \(y^2+\left(3b+2a\right)xy+6abx^2\)
\(=y^2+3bxy+2axy+6abx^2\)
\(=y\left(y+3bx\right)+2ax\left(y+3bx\right)\)
= \(\left(y+2ax\right)\left(y+3bx\right)\)
2, \(ab\left(x-y\right)^2+8ab\)
=\(ab\left(x^2-2xy+y^2\right)+8ab\)
=\(ab\left(x^2-2xy+y^2+8\right)\)
3, \(x^2-\left(2a+b\right)+2aby^2\)
=\(x^2-2axy-bxy+2aby^{2^{ }}\)
=\(\left(x-by\right)\left(x-2ay\right)\)
4, \(xy\left(a^2+2b^2\right)+ab\left(x^2+y^2\right)\)
=\(a^2xy+2x^2ab+y^2ab+2b^2xy\)
=\(\left(ã+yb\right)\left(ay+2xb\right)\)
Phân tích đa thức thành nhân tử ( phối hợp các phương pháp )
1) x2 - ( a + b )xy + aby2
\(=x^2-axy-bxy+aby^2\)
\(=(x^2-axy)-(bxy+aby^2)\)
\(=x(x-ay)-by(x+ay)\)
\(=(x-ay)(x-by)\)
2) x2 + ( 2a + b )xy + 2aby2
=x2 + 2axy + bxy + 2aby2
=(x2+ bxy) +(2axy+ 2aby2 )
=x(x+ by) +2ay(x+ by)
=(x+ by)(x+2ay)
\(a,ax+by+ay+bx=\left(ax+ay\right)+\left(by+bx\right)=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\)
\(b,x^2y+xy+x+1=xy\left(x+1\right)+\left(x+1\right)=\left(xy+1\right)\left(x+1\right)\)
\(c,x^2-ax-bx+ab=x\left(x-a\right)-b\left(x-a\right)=\left(x-b\right)\left(x-2\right)\)
\(d,x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
\(e,a\left(x^2+y\right)-b\left(x^2+y\right)=\left(a-b\right)\left(x^2+y\right)\)
\(f,x\left(a-2\right)-a\left(a-2\right)=\left(x-a\right)\left(a-2\right)\)
a) bạn ktra lại đề
b) \(x^2y+xy+x+1=xy\left(x+1\right)+\left(x+1\right)=\left(xy+1\right)\left(x+1\right)\)
c) \(ax+by+ay+bx=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\)
d) \(x^2-\left(a+b\right)x+ab=x^2-ax-bx+ab=x\left(x-a\right)-b\left(x-a\right)=\left(x-a\right)\left(x-b\right)\)
e) \(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
f) \(ax ^2+ay-bx^2-by=x^2\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x^2+y\right)\)
\(x^2y+xy+x+1\)
\(=xy\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(xy+1\right)\)
hk tốt
^^
bn post nhiều nên mình ghi đáp án thôi nhé phần nào sai đề mình cho qua
b)\(\left(x+1\right)\left(xy+1\right)\)
c)\(\left(a+b\right)\left(x+y\right)\)
d)\(\left(x-a\right)\left(x-b\right)\)
e)\(\left(x+y\right)\left(xy-1\right)\)
f)\(\left(a-b\right)\left(x^2+y\right)\)
x2 - x - y2 - y
= (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
***
9x2 + y2 - 16z2 + 6xy
= (3x + y)2 - (4z)2
= (3x + y - 4z)(3x + y + 4z)
***
a3 - a2x - ay + xy
= a2(a - x) - y(a - x)
= (a - x)(a2 - y)
***
2x2 - 8y2 + 3x + 6y
= 2(x2 - 4y2) + 3(x + 2y)
= 2(x - 2y)(x + 2y) + 3(x + 2y)
= (x + 2y)(2x - 4y + 3)
***
xy(x + y) + yz(y + z) + xz(x + z) + 2xyz
= xy(x + y + z) + yz(x + y + z) + xz(x + z)
= y(x + y + z)(x + z) + xz(x + z)
= (x + z)(xy + y2 + yz + xz)
= (x + z)[y(x + y) + z(x + y)]
= (x + z)(x + y)(y + z)
h) Sửa lại đề bài chút xíu:
$(xy+ab)^2+(ay-bx)^2=x^2y^2+a^2b^2+2abxy+a^2y^2-2aybx+b^2x^2$
$=x^2y^2+a^2b^2+a^2y^2+b^2x^2$
$=(x^2y^2+b^2x^2)+(a^2b^2+a^2y^2)$
$=x^2(y^2+b^2)+a^2(b^2+y^2)=(a^2+x^2)(b^2+y^2)$
j)
$ab(x^2+y^2)+xy(a^2+b^2)=abx^2+aby^2+xya^2+xyb^2$
$=(abx^2+xya^2)+(aby^2+xyb^2)$
$=ax(bx+ay)+by(ay+bx)=(ax+by)(ay+bx)$
k)
$(xy-ab)^2+(bx+ay)^2=x^2y^2-2xyab+a^2b^2+b^2x^2+2bxay+a^2y^2$
$=x^2y^2+a^2b^2+b^2x^2+a^2y^2$
$=(x^2y^2+b^2x^2)+(a^2b^2+a^2y^2)=x^2(y^2+b^2)+a^2(b^2+y^2)$
$=(a^2+x^2)(b^2+y^2)$
e)
$x^2-(2a+b)xy+2aby^2=x^2-2axy-bxy+2aby^2$
$=x(x-2ay)-by(x-2ay)=(x-by)(x-2ay)$
g)
$y^2-(3a+2b)xy+6abx^2=(y^2-2bxy)-(3axy-6abx^2)$
$=y(y-2bx)-3ax(y-2bx)=(y-3ax)(y-2bx)$
f)
$3xy(a^2+b^2)-ab(x^2+9y^2)=3xya^2+3xyb^2-abx^2-9aby^2$
$=(3xya^2-abx^2)-(9aby^2-3xyb^2)$
$=ax(3ay-bx)-3by(3ay-bx)=(3ay-bx)(ax-3by)$