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a ) ( 3x2 + 3x + 2)2 - ( 3x2 + 3x - 2)2
=(3x2 + 3x + 2 + 3x2 + 3x - 2) [( 3x2 + 3x + 2) - ( 3x2 + 3x - 2) ]
=(6x2+6x)*4
=24x(x+1)
b ) ( xy+1)2 - ( x+y)2
=( xy+1 + x+y ) [( xy+1) - ( x+y)]
=[x(y+1)+(y+1)] [x(y-1) - (y-1)]
=(x+1)(y+1)(x-1)(y-1)
c ) ( x + y)3 - ( x - y)3
=[( x + y)-( x - y)] [( x + y)2 - ( x + y)( x - y) + ( x - y)2 ]
=2y( x2+2xy+y2 - x2+y2+ x2-2xy +y2 )
=2y(3y2+x2)
d ) 4( x2 - y2 ) - 8(x - ay) - 4(a2 - 1)
=4(-a2+2ay-y2+x2-2x+1)
=4[-(a-y)2+(x-1)2]
=-4(y-x-a+1)(y+x-a-1)
Mấy bài này khá đơn giản .
Bạn chỉ cần áp dụng hằng đẳng thức \(x^2-y^2=\left(x+y\right)\left(x-y\right)\) là được nhs =))
a)
\(\left(xy+4\right)^2-4\left(x+y\right)^2\)
\(=\left(xy+4\right)^2-\left[2\left(x+y\right)\right]^2\)
\(=\left[xy+4-2\left(x+y\right)\right]\left[xy+4+2\left(x+y\right)\right]\)
\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)
\(=\left[y\left(x-2\right)-2\left(x-2\right)\right]\left[y\left(x+2\right)+2\left(x+2\right)\right]\)
\(=\left(x-2\right)\left(y-2\right)\left(x+2\right)\left(y+2\right)\)
b)
\(\left(ab-xy\right)^2-\left(bx-ay\right)^2\)
\(=\left(ab-xy-bx+ay\right)\left(ab-xy+bx-ay\right)\)
\(=\left[a\left(b+y\right)-x\left(b+y\right)\right]\left[a\left(b-y\right)+x\left(b-y\right)\right]\)
\(=\left(b+y\right)\left(a-x\right)\left(a+x\right)\left(b-y\right)\)
c)
\(=\left(x^2+8x-34+3x^2-8x-2\right)\left(x^2+8x-34-3x^2+8x+2\right)\)
\(=\left(4x^2-36\right)\left(-2x^2+16x-32\right)\)
\(=\left(2x-6\right)\left(2x+6\right)\left(-2\right)\left(x^2-8x+16\right)\)
\(=\left(2x-6\right)\left(2x+6\right)\left(-2\right)\left(x-4\right)^2\)
Bạn liểm tra lại nhs
Mk lm hay nhấm lắm
=))
ảnh giỏi lắm đừng coi thường à. olm tới 11000 điểm mà chỉ 1 tuần dc 1000 đỉm á
a)x2-xy-x+y
=(x2-x)-(xy-y)
=x(x-1)-y(x-1)
=(x-1)(x-y)
b) xy+4-x2+2y
=(4-x2)+(xy+2y)
=(2-x)(x+2)+y(x+2)
=(x+2)(2-x+y)
c) xy+y-2(x+1)
=y(x+1)-2(x+1)
=(x+1)(y-2)
d) 5(x-y)+ax-ay
=5(x-y)+a(x-y)
=(x-y)(5+a)
#H
Trả lời:
a, x2 - xy - x + y
= ( x2 - xy ) - ( x - y )
= x ( x - y ) - ( x - y )
= ( x - y ) ( x - 1 )
b, xy + 4 - x2 + 2y
= ( xy + 2y ) - ( x2 - 4 )
= y ( x + 2 ) - ( x - 2 ) ( x + 2 )
= ( x + 2 ) ( y - x + 2 )
c, xy + y - 2 ( x + 1 )
= y ( x + 1 ) - 2 ( x + 1 )
= ( x + 1 ) ( y - 2 )
d, 5 ( x - y ) + ax - ay
= 5 ( x - y ) + a ( x - y )
= ( 5 + a ) ( x - y )
a)
3x3y2+6x2y4=3x2y2*(x+y2)
b)
16-4x2=4*(4-x2)
c)
xy+xz+5x+5y=(xy+5y)+(xz+5x)
=y*(x+5)+x*(z+5)
=(x+5+z+5)*(y+x)
=5*(x+z)*(x+y)
a) 1/2(x3+8)=1/2(x+2)(x2-2x+4)
b) x4(x-y)+2x3(x-y)=x3(x+2)(x-y)
c) x2-(y2-6y+9)=x2-(y-3)2=(x-y+3)(x+y-3)
d) xy(x3+y3)=xy(x+y)(x2-xy+y2)
e)3x2(x2-25y2)=3x2(x-5y)(x+5y)
f) 4x4+4x2y2+y4-4x2y2= (2x2+y2)2-(2xy)2=(2x2-2xy+y2)(2x2+2xy+y2)
a) \(\frac{1}{2}x^3+4=\frac{1}{2}\left(x^3+8\right)=\frac{1}{2}\left(x+2\right)\left(x^2-2x+4\right)\)
b) \(x^5-x^4y+2x^4-2x^3y=x^3\left(x^2-xy+2x-2y\right)=x^3\left[x\left(x-y\right)+2\left(x-y\right)\right]=x^2\left(x-y\right)\left(x+2\right)\)
c) \(x^2-y^2+6y-9=x^2-\left(y-3\right)^2=\left(x+y-3\right)\left(x-y+3\right)\)
d) \(x^4y+xy^4=xy\left(x^3+y^3\right)=xy\left(x+y\right)\left(x^2-xy+y^2\right)\)
e) \(3x^4-75x^2y^2=3x^2\left(x^2-25y^2\right)=3x^2\left(x+5y\right)\left(x-5y\right)\).
f) \(4x^4+y^4=\left(2x^2+y^2\right)^2-\left(2xy\right)^2=\left(2x^2+y^2+2xy\right)\left(2x^2-y^2-2xy\right)\)
a)\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
b)\(x^4-x^3-x^2+1=\left(x^4-x^3\right)-\left(x^2-1\right)=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
c)\(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)