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\(a,x^2-xy+9x-9y\)
\(=x\left(x-y\right)+9\left(x-y\right)\)
\(=\left(x+9\right)\left(x-y\right)\)
Bài 3:
b: \(x^2+2x+1=\left(x+1\right)^2\)
c: \(x^2-16=\left(x-4\right)\left(x+4\right)\)
d: \(\left(2x-1\right)^2-\left(x+3\right)^2\)
\(=\left(2x-1-x-3\right)\left(2x-1+x+3\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
Bài 1:
a) \(3x-6y=3\left(x-2y\right)\)
b) \(\frac{2}{5}x^2+x^3+x^2y\)
\(=x^2\left(\frac{2}{5}+x+y\right)\)
c) \(14x^2y-21xy^2+28x^2y^2\)
\(=xy\left(14x-21y+28xy\right)\)
d) \(\frac{2}{3}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)\)
\(=\left(y-1\right)\left(\frac{2}{3}x-\frac{2}{5}y\right)\)
e) \(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
f) \(4x^2-25\)
\(=\left(2x\right)^2-5^2\)
\(=\left(2x-5\right)\left(2x+5\right)\)
g) \(6x-9-x^2\)
\(=-x^2+6x-9\)
\(=-\left(x+3\right)^2\)
h) \(x^3+y^3+z^3-3xyz\)
Đề sai ?? ko tách đc nữa
Bài 2:
a) \(15.91,5+150.0,85\)
\(=15.\left(91,5+8,5\right)\)
\(=15.100\)
\(=1500\)
b) \(x\left(x-1\right)-y\left(1-x\right)\)
\(=x\left(x-1\right)+y\left(x-1\right)\)
\(=\left(x-1\right)\left(x+y\right)\)
\(=2000.4000\)
\(=8000000\)
c) \(87^2+73^2-27^2-13^2\)
\(=\left(87^2-27^2\right)+\left(73^2-13^2\right)\)
\(=\left(87-27\right)\left(87+27\right)+\left(73-13\right)\left(73+13\right)\)
\(=60.114+60.86\)
\(=60.\left(144+86\right)\)
\(=60.230\)
\(=82800\)
d) \(73^2-27^2\)
\(=\left(73-27\right)\left(73+27\right)\)
\(=46.100\)
\(=4600\)
e) f) tương tự
a) \(x-xy+y-y^2=x\left(1-y\right)+y\left(1-y\right)=\left(x+y\right)\left(1-y\right)\)
b) \(x^2-2x-y^2+1=\left(x^2-2x+1\right)-y^2=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\)
c) \(4x^2-4xy+y^2=\left(2x\right)^2-2.2x.y+y^2=\left(2x-y\right)^2\)
d) \(9x^3-9x^2y-4x+4y=9x^2\left(x-y\right)-4\left(x-y\right)=\left(9x^2-4\right)\left(x-y\right)=\left(3x-2\right)\left(3x+2\right)\left(x-y\right)\)
e) \(x^3+2+3\left(x^3-2\right)=x^3+2+3x^3-6=4x^3-4=4\left(x^3-1\right)=4\left(x-1\right)\left(x^2+x+1\right)\)
Bài 3:
a: =>(2x-7)(x-2)=0
=>x=7/2 hoặc x=2
b: =>(x-1)(x+2)=0
=>x=1 hoặc x=-2
d: =>2x+3=0
hay x=-3/2
a) x\(^2\)- xy + 9x -9y = x( x + 9 ) - y ( x + 9 ) = (x - y ) ( x + 9 )
b) x\(^2\)- 2xy - 5x + 10y = x ( x - 5 ) - 2y ( x - 5 ) = ( x - 2y ) ( x - 5 )
d) x\(^2\)+ 4x - y\(^2\)+ 4y = x\(^2\) - y\(^2\) + 4 ( x + y ) = ( x+ y ) ( x- y ) + 4 ( x+ y )
= (x+ y ) ( x - y + 4 )
e) 37,5×6,5-7,5×3,4-6,6×7,5+3,5×37,5
= ( 37,5. 6,5 + 3,5 . 37,5 ) - ( 7,5 . 3,4 + 6,6 . 7,5 )
= 37,5 ( 6,5 + 3,5 ) - 7,5 ( 3,4 + 6,6 )
= 37,5 . 10 - 7,5 . 10
= 375 - 75 = 300