Phân tích đa thức thành nhân tử :
a ) 9xyz+18xy^2z^2 – 27y^2 z
b ) 4x(x-2y)+8y(2y-x)
c ) 4x^2(x-y ) – 10y( y-x)
d ) x(x-1) + (1-x)^2
e ) 10-x^2-25
g ) 25-(3-x)^2
Phân tích đa thức thành nhân tử :
a ) 9xyz+18xy^2z^2 – 27y^2 z
b ) 4x(x-2y)+8y(2y-x)
c ) 4x^2(x-y ) – 10y( y-x)
d ) x(x-1) + (1-x)^2
e ) 10-x^2-25
g ) 25-(3-x)^2
a) `9xyz + 18xy^2 z^2 – 27y^2 z = 9yz ( x + 2yz – 3y)`
b) `4x(x-2y) +8y(2y-x) = 4x(x-2y) – 8y(x-2y)`
`= (x-2y)(4x-8y) = 4(x-2y)(x-2y) = 4(x-2y)^2`
c) `4x^2 (x-y) – 10y (y-x) = 4x^2 (x-y)+ 10y (x-y) = (x-y)(4x^2+10y)`
d) `x(x-1) + (1-x)^2 = x(x-1) + (x-1)^2 = (x-1)(x+x-1) = (x-1)(2x-1)`
e) `10x – x^2 – 25 = -(x^2 – 2.x.5 + 5^2) = -(x-5)^2`
g) `25-(3-x)^2 = 5^2 – (3-x)^2 = (5+3-x)(5-3+x) = (8-x)(2+x)`
a) `9xyz+18xy²z²-27y²z`
`= 9yz(x+2xyz-3y)`
b) `4x(x-2y)+8y(2y-x)`
`= 4x(x-2y)-8y(x-2y)`
`= (4x-8y)(x-2y)`
c) `4x²(x-y)-10y(y-x)`
`= 4x²(x-y)+10y(x-y)`
`= (4x²+10y)(x-y)`
d) `x(x-1)+(1-x)²`
`= x(x-1)-(x-1)²`
`= (x-x-1)(x-1)`
`= -1(x-1)`
e) `10x-x²-25`
`= -(x²-2.x.5-5²)`
`= -(x-5)²`
g) `25-(3-x)²`
`= 5²-(3-x)²`
`= (5+3-x)(5-3+x)`
`= (8-x)(2+x)`