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a. \(2a^2+5ab-3b^2-7b-2\)
\(=\left(2a^2+6ab+2a\right)-\left(ab+3b^2+b\right)-\left(2a+6b+2\right)\)
\(=2a\left(a+3b+1\right)-b\left(a+3b+1\right)-2\left(a+3b+1\right)\)
\(=\left(2a-b-2\right)\left(a+3b+1\right)\)
b. \(2x^2-7xy+x+3y^2-3y\)
\(=\left(2x^2-xy\right)-\left(6xy-3y^2\right)+\left(x-3y\right)\)
\(=x\left(2x-y\right)-3y\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y+1\right)\)
c. \(6x^2-xy-2y^2+3x-2y\)
\(=\left(6x^2+3xy\right)-\left(4xy-2y^2\right)+\left(3x-2y\right)\)
\(=3x\left(2x+y\right)-2y\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y+1\right)\)
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a/ \(12x^2+5x-12y^2+12y-10xy-3.\)
\(=12x^2+9x-4x-12y^2+6y+6y-18xy+8xy-3.\)
\(=\left(12x^2-18xy+9x\right)-\left(4x-6y+3\right)+\left(8xy-12y^2+6y\right)\)
\(=3x\left(4x-6y+3\right)-\left(4x-6y+3\right)+2y\left(4x-6y+3\right)\)
\(=\left(4x-6y+3\right)\left(3x-1+2y\right)\)
2/ \(2x^2+y^2+3x-2y-3xy+1\)
\(=\left(y^2-2y+1\right)+\left(3x-3xy\right)+2x^2\)
\(=\left(y-1\right)^2+3x\left(1-y\right)+2x^2\)
\(=\left(y-1\right)^2-3x\left(y-1\right)+2x^2\)
Bài làm
a) 4x - 8y
<=> 4( x - 2y )
b) 12x( x - 2y ) - 8y( x - 2y )
<=> ( 12x - 8y )( x - 2y )
<=> 4( 3x - 2y )( x - 2y )
c) 2x + 2y - x2 - xy
= 2( x + y ) - x( x + y )
= ( x + y )( 2 - x )
d) x2 - 4y2
<=> ( x - 2y )( x + 2y )
e) x3 + x2y - 4x - 4y
<=> x2( x + y ) - 4( x + y )
<=> ( x - 2 )( x + 2 )( x + y )
g) 3x2 - 6xy + 3y2 - 12x3
<=>3( x2 - 3xy + y2 - 4x3 )
# Học tốt #
a)4(x-2y)
b)(x-2y)(12x-8y)
=4(x-2y)(3x-2y)
c)2(x+y)-x(x+y)
=(2-x)(x+y)
d)(x-2y)(x+2y)
e)x2(x+y)-4(x+y)
=(x+y)(x2-4)
=(x+y)(x-2)(x+2)
g)3(x2-2xy+y2-4z3)
=3[(x-y)2-4z3]
????????????phải là 4z2chứ nhỉ.....
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)