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a) \(3xy-6xy^2=3xy\left(1-2y\right)\)
b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)
c) \(x^3-x^2+2\)
d) \(x^2+4x+4-y^2=\left(x^2+4x+4\right)-y^2=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)
e) \(x^3+4x^2+4x=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)
f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)
g) \(6x^2-12x=6x\left(x-2\right)\)
h) \(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)
i) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
Bài 3:
a) \(\left(4x^2+4xy+y^2\right):\left(2x+y\right)=\left(2x+y\right)^2:\left(2x+y\right)=2x+y\)
b) \(\left(27x^3+1\right):\left(3x+1\right)=\left(3x+1\right)\left(9x^2-9x+1\right):\left(3x+1\right)=9x^2-9x+1\)
c) \(\left(x^2-6xy+9y^2\right):\left(3y-x\right)=\left(x-3y\right)^2:\left(3y-x\right)=\left(3y-x\right)^2:\left(3y-x\right)=3y-x\)
d) \(\left(8x^3-1\right):\left(4x^2+2x+1\right)=\left(2x-1\right)\left(4x^2+2x+1\right):\left(4x^2+2x+1\right)=2x-1\)
Bài 4: Tương tự bài 3 '-'
Bài 4 :
a ) ( 4x4 - 9 ) : ( 2x2 - 3 )
= ( 2x2 + 3 )( 2x2 - 3 ) : ( 2x2 - 3 )
= 2x2 + 3
b ) ( 8x3 - 27 ) : ( 4x2 + 6x + 9 )
= ( 2x - 3 )( 4x2 + 6x + 9 ) : ( 4x2 + 6x + 9 )
= 2x - 3
a) x^2+2xy+y^2-16
=(x+y)2-16
=(x+y-4)(x+y+4)
b) 3x^2+5x-3xy-5y
=(3x2-3xy)+(5x-5y)
=3x(x-y)+5(x-y)
=(x-y)(3x+5)
c) 4x^2-6x^3y-2x^2+8x
ko bik hoặc sai đề
d) x^2-4-2xy+y^2
=(x-y)2-4
=(x-y+2)(x-y-2)
e) x^3-4x^2-12x+27
=sai đề
g) 3x^2-18x+27
=3(x2-6x+9)
=3(x-3)2
h) x^2-y^2-z^2-2yz
=x2-(y2+z2+2yx)
=x2-(y+z)2
=(x-y-z)(x+y+z)
k) 4x^2(x-6)+9y^2(6-x)
=4x2(x-6)-9y2(x-6)
=(x-6)(4x2-9y2)
=(x-6)(2x-3y)(2x+3y)
l)6xy+5x-5y-3x^2-3y^2
=(5x-5y)+(-3x2+6xy-3y2)
=5(x-y)-3(x2-2xy+y2)
=5(x-y)-3(x-y)2
=(x-y)(5-3(x-y))
=(x-y)(5-3x+3y)
a) \(\left(x+6\right)^2-x\left(x+9\right)=0\)
\(\Leftrightarrow\)\(x^2+12x+36-x^2-9x=0\)
\(\Leftrightarrow\)\(3x+36=0\)
\(\Leftrightarrow\)\(x=-12\)
Vậy...
b) \(6x\left(2x+5\right)-\left(3x+4\right)\left(4x-3\right)=9\)
\(\Leftrightarrow\)\(12x^2+30x-12x^2-7x+12=9\)
\(\Leftrightarrow\)\(23x+12=9\)
\(\Leftrightarrow\)\(x=-\frac{3}{23}\)
Vậy
c) \(2x\left(8x+3\right)-\left(4x+1\right)=13\)
\(\Leftrightarrow\)\(16x^2+6x-4x-1=13\)
\(\Leftrightarrow\)\(16x^2+2x-14=0\)
\(\Leftrightarrow\)\(8x^2+x-7=0\)
\(\Leftrightarrow\)\(\left(x+1\right)\left(8x-7\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=-1\\x=\frac{7}{8}\end{cases}}\)
Vậy
d) \(\left(x-4\right)^2-x\left(x+4\right)=0\)
\(\Leftrightarrow\)\(x^2-8x+16-x^2-4x=0\)
\(\Leftrightarrow\)\(-12x+16=0\)
\(\Leftrightarrow\)\(x=\frac{4}{3}\)
Vậy
e) \(\left(x-2\right)^2-\left(2x+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\)\(x^2-4x+4-2x^2+x+6=0\)
\(\Leftrightarrow\)\(-x^2-3x+10=0\)
\(\Leftrightarrow\)\(\left(2-x\right)\left(x+5\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=2\\x=-5\end{cases}}\)
Vậy
a) (x2-6xy+9y2):(3y-x)
= (x-3y)2:(3y-x)
=(3y-x)2:(3y-x)
= 3y-x
b) (8x3-1):(4x2+2x+1)
=[(2x)3-1]:(4x2+2x+1)
= (2x-1)(4x2+2x+1):(4x2+2x+1)
= 2x-1
c) (4x4-9):(2x2-3)
=(2x2-3)(2x2+3):(2x2-3)
=2x2+3
d) (8x3-27):(4x2+6x+9)
=(2x-3)(4x2+6x+9):(4x2+6x+9)
=2x-3