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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) \(x^3-x^2-x+1\)
\(=\left(x^3-x^2\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-1\right)\)
b) \(x^3-3x+1-3x^2\)
\(=\left(x^3+1\right)-\left(3x^2+3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
c) \(x^2-4x-5\)
\(=x^2.2x.2+4-9\)
\(=\left(x-2\right)^2-3^2\)
\(=\left(x-2+3\right)\left(x-2-3\right)\)
\(=\left(x+1\right)\left(x-5\right)\)
c) x2 - 4x - 5
= x2-5x+x-5
=(x2-5x)+(x-5)
=x(x-5)+(x-5)
=(x-5)(x+1)
a) Đề bài phải là : \(\left(x+y\right)^2-\left(x-y\right)^2\)thì mới phân tích được.
Nếu đề bài như trên ta có:
\(\left(x+y\right)^2-\left(x-y\right)^2=\)\(\left(x+y-x+y\right)\left(x+y+x-y\right)=2x\cdot2y=4xy\)
b) Ta có: \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)\)
= \(2x\cdot\left(4x+2\right)=2x\cdot2\cdot\left(2x+1\right)=4x\cdot\left(2x+1\right)\)
c) Ta có : \(x^3+y^3+z^3-3xyz\)
= \(\left(x+y\right)^3+z^3-3x^2y-3xy^2-3xy\)
=\(\left(x+y+z\right)\left(\left(x+y\right)^2-\left(x+y\right)z+z^2\right)-3xy\left(x+y+z\right)\)
=\(\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)
=\(\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
a) \(2x^2+3x-5=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
b) \(\left(x+y+z\right)^3-x^3-y^3-z^3\)
\(=\left(x+y\right)^3+3z\left(x+y\right)\left(x+y+z\right)+z^3-x^3-y^3-z^3\)
\(=x^3+y^3+z^3+3xy\left(x+y\right)+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)
\(=3\left(x+y\right)\left[xy+z\left(x+y+z\right)\right]\)
\(=3\left(x+y\right)\left(xy+xz+yz+z^2\right)\)
\(=3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
c) \(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
d) \(x^4-x^3-x^2+1=x^2\left(x-1\right)-\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left(x^2-x-1\right)\)
e) \(x^4+4x^2-5=\left(x^2+2\right)^2-9=\left(x^2+2+3\right)\left(x^2+2-3\right)=\left(x^2+5\right)\left(x+1\right)\left(x-1\right)\)