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a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
\(B=7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(7x-5\right)\)
\(E=x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
\(F=x^2-9x+18\)
\(=x^2-3x-6x+18\)
\(=x\left(x-3\right)-6\left(x-3\right)\)
\(=\left(x-3\right)\left(x-6\right)\)
\(H=8x^2-2x-1\)
\(=8x^2-4x+2x-1\)
\(=4x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(2x-1\right)\left(4x+1\right)\)
a) \(x^4-2x^2+1=\left(x^2-1\right)^2=\left(x-1\right)^2\left(x+1\right)^2\)
b) \(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
c) \(2x^3-x^2-8x+4\)
\(=x^2\left(2x-1\right)-4\left(2x-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(2x-1\right)\)
d) \(x\left(x-y\right)^2+y\left(x-y\right)^2-xy+x^2\)
\(=\left(x+y\right)\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2+x\right)\)
e) \(2x^2-5x+2\)
\(=\left(2x^2-x\right)-\left(4x-2\right)\)
\(=x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(x-2\right)\left(2x-1\right)\)
a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
Bài làm
a) 4x2 - 6x
= 2x( 2x - 3 )
b) 9x4y3 + 3x2y4
= 3x2y3( 3x2 + y )
c) x3 - 2x2 + 5x
= x( x2 - 2x + 5 )
d) 3x( x - 1 ) + 5( x - 1 )
= ( x - 1 )( 3x + 5 )
e) 2x2( x + 1 ) + 4( x + 1 )
= ( x + 1 )( 2x2 + 4 )
= ( x + 1 )2( x2 + 2 )
= 2( x + 1 )( x2 + 2 )
f) -3x - 6xy + 9xz
= -( 3x + 6xy - 9xz )
= -3x( 1 + 2y - 3z )
# Học tốt #
a/ 5x2y - 2xy
= xy.(5x-2)
b/ x2 - 6x + 9
= x2 - 2.3.x + 32
= (x-3)2
c/ 8x3 - 27
= (2x)3 - 33
= (2x - 3).[(2x)2 - 2x.3 + 32]
= (2x-3).(4x2 - 6x + 9)
d/ x2 - 2x - 25y2 + 1
= (x2 - 2x + 1) - 25y2
= (x-1)2 - (5y)2
= (x-1-5y).(x-1+5y)
e/ 6x2 - x - 5
= 6x2 + 6x - 5x - 5
= 6x.(x+1) - 5.(x+1)
= (x+1).(6x-5)
f/ (2x -y).(x+3) - 5.(y-2x)
= (2x-y).(x+3) + 5.(2x-y)
= (2x-y).(x+3+5)
= (2x-y).(x+8)
g/ (x+y)2 - z2
= (x+y-z).(x+y+z)
k/ x3 - 4x2 + 4x
= x.(x2 - 4x + 4)
= x.(x2 - 2.x.2 + 22)
= x.(x-2)2
m/ 5x2 - x + y - 5y2
= 5x2 - 5y2 - (x-y)
= 5.(x2 - y2) - (x-y)
= 5.(x+y).(x-y) - (x-y)
= (x-y).[5(x+y) - 1]
i/ x2 + 9x - 10
= x2 - x + 10x - 10
= x.(x-1) + 10.(x-1)
= (x-1).(x+10)
a)5x2y-2xy=xy(5x-2)
b)x2-6x+9=x2-2.x.3+32=(x-3)2
c)8x3-27=(2x)3-33=(2x-3)(4x2+6x+9)
d)x2-2x-25y2+1=(x2-2x+1)-25y2=(x-1)2-25y2
=(x-1-5y)(x-1+5y)
e)6x2-x-5=6x2-6x+5x-5=(6x2-6x)+(5x-5)=6x(x-1)+5(x-1)=(x-1)(6x+5)
f)(2x-y)(x+3)-5(y-2x)=(2x-y)(x+3)-5(2x-y)=(2x-y)(x+3-5)=(2x-y)(x-2)
g)(x+y)2-z2=(x+y+z)(x+y-z)
k)x3-4x2+4x=x(x2-4x+4)=x(x-2)2
m)5x2-x+y-5y2=(5x2-5y2)-(x-y)=5(x2-y2)-(x-y)=5(x-y)(x+y)-(x-y)
=5(x-y)(x+y+1)
i)x2+9x-10=x2-x+10x-10=(x2-x)+(10x-10)=x(x-1)+10(x-1)=(x-1)(x+10)
a,\(5x^2y-2xy\)
\(=xy\left(5x-2\right)\)
b,\(x^2-6x+9\)
\(=x^2-2.x.3+3^2\)
\(=\left(x-3\right)^2\)
c,\(8x^3-27\)
\(=\left(2x\right)^3-3^3\)
\(=\left(2x-3\right)\left(4x^2+6x+9\right)\)
d,\(x^2-2x-25y^2+1\)
\(=x^2-2x+1-25y^2\)
\(=\left(x-1\right)^2-\left(5y\right)^2\)
\(\left(x-1-5y\right)\left(x-1+5y\right)\)
e,\(6x^2-x-5\)
\(=6x^2-6x+5x-5\)
\(=\left(6x^2-6x\right)+\left(5x-5\right)\)
\(=6x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(6x+5\right)\left(x-1\right)\)
f,\(\left(2x-y\right)\left(x+3\right)-5\left(y-2x\right)\)
\(=\left(2x-y\right)\left(x+3\right)+5\left(2x-y\right)\)
\(=\left(2x-y\right)\left(x+3+5\right)\)
g,\(\left(x+y\right)^2-z^2\)
\(=\left(x+y-z\right)\left(x+y+z\right)\)
k,\(x^3-4x^2+4x\)
\(=x\left(x^2-4x+4\right)\)
\(=x\left(x-2\right)^2\)
m,\(5x^2-x+y-5y^2\)
\(=\left(5x^2-5y^2\right)+\left(-x+y\right)\)
\(=5\left(x^2-y^2\right)-\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y-1\right)\)
(Câu này mình chưa chắc lắm,bạn xem lại nhé)
i,\(x^2+9x-10\)
\(=x^2+10x-x-10\)
\(=\left(x^2-x\right)+\left(10x-10\right)\)
\(=x\left(x-1\right)+10\left(x-1\right)\)
\(=\left(x+10\right)\left(x-1\right)\)
Chúc bạn học tốt!!!
a) 5x2y - 2xy = xy(5x - 2)
b) x2 - 6x + 9 = (x - 3)2
c) 8x3 - 27 = (2x - 3)(4x2 + 6x + 9)
d) x2 - 2x - 25y2 + 1
= x2 - 2x + 1 - 25y2
= (x - 1)2 - (5y)2
= (x - 1 - 5y)(x - 1 + 5y)
e) 6x2 - x - 5
= 6x2 + 6x - 5x - 5
= 6x(x + 1) - 5(x + 1)
= (x + 1)(6x - 5)
f) (2x - y)(x + 3) - 5(y - 2x)
= (2x - y)(x + 3) + 5(2x - y)
= (2x - y)(x + 3 + 5)
= (2x - y)(x + 8)
g) (x + y)2 - z2
= (x + y - z)(x + y + z)
k) x3 + 4x2 + 4x
= x(x2 + 4x + 4)
= x(x + 2)2
m) 5x2 - x + y - 5y2
= 5x2 - 5y2 - x + y
= 5(x2 - y2) - (x - y)
= 5(x - y)(x + y) - (x - y)
= (x - y)(5x + 5y - 1)
i) x2 + 9x - 10
= x2 - x + 10x - 10
= x(x - 1) + 10(x - 1)
= (x - 1)(x + 10)
câu m kết quả sửa +1 thành -1, mk nhầm