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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. \(6x^2-xy-2y^2+3x-2y\)
\(=\left(6x^2+3xy\right)-\left(4xy-2y^2\right)+\left(3x-2y\right)\)
\(=3x\left(2x+y\right)-2y\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y+1\right)\)
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/ \(2x^2+y^2+3x-2y-3xy+1\)
\(=\left(y^2-2y+1\right)+\left(3x-3xy\right)+2x^2\)
\(=\left(y-1\right)^2+3x\left(1-y\right)+2x^2\)
\(=\left(y-1\right)^2-3x\left(y-1\right)+2x^2\)
a) 4x2 - 5xy + y2 = 4x2 - 4xy - xy + y2 = 4x( x - y ) - y( x - y ) = ( x - y )( 4x - y )
b) x2 - 4xy + 3y2 = x2 - xy - 3xy + 3y2 = x( x - y ) - 3y( x - y ) = ( x - y )( x - 3y )
c) 9x2 + 6xy - 8y2 = 9x2 - 6xy + 12xy - 8y2 = 9x( x - 2/3y ) + 12y( x - 2/3y ) = ( x - 2/3y )( 9x + 12y )
d) 2x2 + 3xy - 5y2 = 2x2 - 2xy + 5xy - 5y2 = 2x( x - y ) + 5y( x - y ) = ( x - y )( 2x + 5y )
e) x2 - 35y2 - 2xy = x2 + 5xy - 7xy - 35y2 = x( x + 5y ) - 7y( x + 5y ) = ( x + 5y )( x - 7y )
f) 2x2 + 10xy + 8y2 = 2( x2 + 5xy + 4y2 ) = 2( x2 + xy + 4xy + 4y2 ) = 2[ x( x + y ) + 4y( x + y ) ] = 2( x + y )( x + 4y )
g) x2 - 10xy + 16y2 = x2 - 2xy - 8xy + 16y2 = x( x - 2y ) - 8y( x - 2y ) = ( x - 2y )( x - 8y )
h) 4x2 + 4xy - 15y2 = 4x2 - 6xy + 10xy - 15y2 = 4x( x - 3/2y ) + 10y( x - 2/3y ) = ( x - 2/3y )( 4x + 10y )
i) -7xy + 3x2 + 2y2 = 3x2 - xy - 6xy + 2y2 = 3x( x - 1/3y ) - 6y( x - 1/3y ) = ( x - 1/3y )( 3x - 6y )
j) 56y2 + 4x2 - 36xy = 4( x2 - 9xy + 14y2 ) = 4( x2 - 2xy - 7xy + 14y2 ) = 4[ x( x - 2y ) - 7y( x - 2y ) ] = 4( x - 2y )( x - 7y )
D ez nhất :v
\(D=\left(x^2-2x+1\right)+\left(y^2+4y+4\right)+5\)
\(=\left(x-1\right)^2+\left(y+2\right)^2+5\ge5\)
Đẳng thức xảy ra khi x = 1 và y = -2
\(A=\left[\left(x^2-2xy+y^2\right)+4\left(x-y\right)+4\right]+\left(y^2-2y+1\right)+2020\)
\(=\left[\left(x-y\right)^2+2\left(x-y\right).2+2^2\right]+\left(y-1\right)^2+2020\)
\(=\left(x-y+2\right)^2+\left(y-1\right)^2+2020\ge2020\)
Dấu "=" xảy ra khi y = 1 và x - y + 2 = 0 tức là x = y - 2 = -1
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.....
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