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Đổi dấu – (4yx2 + yz2)(z – y2) = (4yx2 + yz2)( y2 – z), ta có thừa số
(y2 – z) chung:
C = (y2 – z)(2x2y – yz) – (4yx2 + yz2)(z – y2) + 6x2z(y2 – z)
= (y2 – z)(2x2y – yz) + (4yx2 + yz2)( y2 – z) + 6x2z(y2 – z)
= (y2 – z)[( 2x2y – yz ) + (4yx2 + yz2) + 6x2z]
= (y2 – z)[ 2x2y + 4yx2 + 6x2z]
= (y2 – z)[ 2xy2 + 4yx2 + 6x2z]
= (y2 – z)[ 2x2(y + 2y + 3z)]
= (y2 – z)[ 2x2(3y + 3z)]
= (y2 – z) 2x2 .3(y + z)
= 6x2(y2 – z)(y + z).
a) 7x2 - 4x
= x ( 7x - 4 )
b) 5x2 - 2x + 10 xy - 4y
= x ( 5x - 2 ) + 2y ( 5x - 2 )
= ( x + 2y ) ( 5x - 2 )
Ta nhân thấy nghiệm của f(x) nếu có thì x = 
Cách 1:
x3 – x2 – 4 =(x3-2x2)+(x2-2x)+(2x-4)=x2(x-2)+x(x-2)+2(x-2)=(x-2)(x2+x+2)
Cách 2:
(x-2)[(x2+2x+4)-(x+2)]=(x-2)(x2+x+2)
x3-x2-4=x3-8-x2+4=(x3-8)-(x2-4)=(x-2)(x2+2x+4)-(x-2)(x+2)
b = x.(x2 + 6x + 9 - 4y2 ) =x.((x+3)2 -4y2 )= x.(x+3-2y).(x+3+2y)
c = (x2 - 2x)+(2y-xy) = x.(x-2) +y.(2-x)= x.(x-2) + y.(-x+2)= x.(x-2) - y.(x-2) = (x-y).(x-2)
d = (x2 +1)2 - 4x2 = (x2 + 1 - 2x).(x2 +1 +2x) = (x-1)2 . (x+1)2
a = (7x)2 - (0.5y)2 = (7x - 0,5y).(7x+0,5y)
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) \(\left(x^2-2x+1\right)-\left(y^2+2y+1\right)\)
\(=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-y-2\right)\left(x+y\right)\)
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.....
\(a, 4x^2-4y^2\)
\(= (4x-4y)(4x+4y)\)
\(b. x^2-xy+2x-2y\)
\(= (x^2-xy)+(2x-2y)\)
\(=x(x-y)+2(x-y)\)
\(=(x+2)(x-y)\)
\(c, 6x^2-7x+2\)
\(= 6x^2-4x-3x+2\)
\(=(6x^2-4x)-(3x-2)\)
\(= 2x(3x-2)-(3x-2)\)
\(=(3x-2)(2x-1)\)
phần a Sai rồi bạn nhá mik sửa cho:
\(a.4x^2-4y^2\\ =4\left(x^2-y^2\right)\\ =4\left(x-y\right)\left(x+y\right)\)
Bạn nên cẩn thận hơn ở những lần sau :))