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a) \(6x\left(x-y\right)-3\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(2x-x+y\right)\)
b) \(2a\left(x-1\right)+b\left(x-1\right)-\left(1-x\right)\)
\(=2a\left(x-1\right)+b\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(2a+b+1\right)\)
c) \(2x\left(x-2\right)-\left(x-2\right)^2+5x\left(2-x\right)\)
\(=2x\left(x-2\right)-\left(x-2\right)^2-5x\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-x+2-5x\right)\)
\(=\left(x-2\right)\left(-4x+2\right)\)
những bài này dễ lắm bn à, chỉ đơn thuần là áp dụng hđt thui
a) (x+1)(4x-8) =0
x+1=0
x= -1
4x-8 =0
x = 2
b) = 2(x+1)(x+1) = 2(x+1)2
..........................
a) \(2x\left(x-3\right)^2+5x\left(3-x\right)\)
\(=2x\left(x-3\right)^2-5x\left(x-3\right)\)
\(=\left(x-3\right)\left[2x\left(x-3\right)-5x\right]\)
\(=\left(x-3\right)\left(2x^2-6x-5x\right)\)
\(=\left(x-3\right)\left(2x^2-11x\right)\)
\(=x\left(x-3\right)\left(2x-11\right)\)
b) \(\left(x+3\right)^2-4\left(y^2-2y+1\right)\)
\(=\left(x+3\right)^2-2^2\left(y-1\right)^2\)
\(=\left(x+3\right)^2-\left[2\left(y-1\right)\right]^2\)
\(=\left[\left(x+3\right)-2\left(y-1\right)\right]\left[\left(x+3\right)+2\left(y-1\right)\right]\)
\(=\left(x+3-2y+2\right)\left(x+3+2y-2\right)\)
\(=\left(x-2y+5\right)\left(x+2y+1\right)\)
a) \(2x.\left(x-3\right)^2+5x.\left(-x+3\right)=2x.\left(x-3\right)^2-5x.\left(x-3\right)\)
\(=\left(x-3\right).\left(2x^2-11x\right)=\left(x-3\right).x.\left(2x-11\right)\)
b) \(\left(x+3\right)^2-4.\left(y^2-2y+1\right)=\left(x+3\right)^2-2^2.\left(y-1\right)^2\)
\(=\left(x+3\right)^2-\left[2.\left(y-1\right)\right]^2=\left(x-2y+1\right).\left(x+2y+5\right)\)
a) \(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=3x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\)
Bài làm
a) 4x2 - 6x
= 2x( 2x - 3 )
b) 9x4y3 + 3x2y4
= 3x2y3( 3x2 + y )
c) x3 - 2x2 + 5x
= x( x2 - 2x + 5 )
d) 3x( x - 1 ) + 5( x - 1 )
= ( x - 1 )( 3x + 5 )
e) 2x2( x + 1 ) + 4( x + 1 )
= ( x + 1 )( 2x2 + 4 )
= ( x + 1 )2( x2 + 2 )
= 2( x + 1 )( x2 + 2 )
f) -3x - 6xy + 9xz
= -( 3x + 6xy - 9xz )
= -3x( 1 + 2y - 3z )
# Học tốt #
a)x4-1=(x2-1)(x2+1)=(x-1)(x+1)(x2+1)
b)x2-y2-2x+2y=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)
c)x2-6x-y2+9=(x2-6x+9)-y2=(x-3)2-y2=(x-y-3)(x+y-3)
d)5x2+3(x+y)2-5y2
=5(x2-y2)+3(x+y)2
=5(x-y)(x+y)+3(x+y)2
=(x+y)(5x-5y+3x+3y)
=(x+y)(8x-2y)
a) 2x2-6x-x+3 = 2x(x-3) - (x-3) = (x-3)(2x-1)
b) x2-x-5x+5 = x(x-1) - 5(x-1) = (x-1)(x-5)
c) 5x(x-2y) + 2( x-2y)2 = (x-2y)(5x+2x-2y) = (x-2y)(7x-2y)
chú ý : (A-B)2=(B-A)2
d) 7x(4-y)2 - (4-y)3 = ( 16-8y+y2) (7x-4+y)
a) \(2x^2-7x+3=2x^2-6x-x+3=2x\left(x-3\right)-\left(x-3\right)=\left(x-3\right)\left(2x-1\right)\)
b) \(x^2-6x+5=x^2-5x-x+5=x\left(x-5\right)-\left(x-5\right)=\left(x-5\right)\left(x-1\right)\)
c)\(5x\left(x-2y\right)+2\left(2y-x\right)^2=5x\left(x-2y\right)+2\left(x-2y\right)^2\\ =\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
d) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)+\left(y-4\right)^3=\left(y-4\right)\left(7x-y-4\right)\)
a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
a) \(6\text{x}\left(x-y\right)-3\left(x-y\right)^2\)
\(=\left(x-y\right)\left(6\text{x}-3\text{x}+3y\right)\)
\(=\left(x-y\right)\left(3\text{x}+3y\right)\)
\(=3\left(x-y\right)\left(x+y\right)\)
\(=3\left(x^2-y^2\right)\)
b) \(2\text{a}\left(x-1\right)+b\left(x-1\right)-\left(1-x\right)\)
\(=2\text{a}\left(x-1\right)+b\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(2\text{a}+b+1\right)\)
c) \(2\text{x}\left(x-2\right)-\left(x-2\right)^2+5\text{x}\left(2-x\right)\)
\(=2\text{x}\left(x-2\right)-\left(x-2\right)^2-5\text{x}\left(x-2\right)\)
\(=\left(x-2\right)\left(2\text{x}-x+2-5\text{x}\right)\)
\(=\left(x-2\right)\left(2-4\text{x}\right)\)