Bài 1: Phân tích đa thức thành nhân tử:
a) 3x2 -6xy +3y2 -12z2
b) x2 -25 +y2 +2xy
Phân tích các đa thức sau thành nhân tử:
a) 3x4y - 12x2y3
b) x2 - y2 - 8y -16
c) x3 +3x2 + 4x +12
d) 3x2 - 6xy + 3y2 - 27
\(3x^4y-12x^2y^3=3x^2y\left(x^2-4y^2\right)=3x^2y\left(x-2y\right)\left(x+2y\right)\)
\(x^2-y^2-8y-16=x^2-\left(y^2+8y+16\right)=x^2-\left(y+4\right)^2=\left(x+y+4\right)\left(x-y-4\right)\)
\(x^3+3x^2+4x+12=x^2\left(x+3\right)+4\left(x+3\right)=\left(x^2+4\right)\left(x+3\right)\)
\(3x^2-6xy+3y^2-27=3\left[\left(x-y\right)^2-9\right]=3\left(x-y-3\right)\left(x-y+3\right)\)
Bài 1: Phân tích đa thức thành nhân tử.
a) A = 3x2 + 6xy + 3y2 - 3z2
b) A = ( x + y )2 - 2 ( x + y ) + 1
c) A = x2 + y2 + 2xy + yz + zx
a)\(A=3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-z\right)\left(x+y+z\right)\)b) \(A=\left(x+y\right)^2-2\left(x+y\right)+1=\left(x+y-1\right)^2\)
c) \(A=x^2+y^2+2xy+yz+zx=\left(x+y\right)^2+z\left(x+y\right)=\left(x+y\right)\left(x+y+z\right)\)
Bài 1: Phân tích đa thức thành nhân tử:
a) x2 -2x -y2 +2y
b) 2x +2y -x2 -xy
c) 3x2 -6xy +3y2 -12z2
d) x2 -25 +y2 +2xy
a) x2-2x-y2+2y
=(x2-y2)-(2x-2y)
=(x-y)(x+y)-2(x-y)
=(x-y)(x+y-2)
d) x2-25+y2+2xy
=(x2+y2+2xy)-52
=(x+y)2-52
=(x+y+5)(x+y-5)
Bài 2*: Phân tích đa thức thành nhân tử:
a) 3x2-3y2-2(x-y)2
b) x2-y2-2x-2y
c) (x-1)(2x+1)+3(x-1)(x+2)(2x+1)
d) (x-5)2+(x+5)(x-5)-(5-x)(2x+1)
\(a.3x^2-3y^2-2\left(x-y\right)^2\\ =3\left(x^2-y^2\right)-2\left(x-y\right)^2\\ =3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\\ =\left(x-y\right)\left[3\left(x+y\right)-2.\left(x-y\right)\right]=\left(x-y\right)\left(x+5y\right)\\ b.x^2-y^2-2x-2y\\ =\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\\ =\left(x+y\right)\left(x-y-2\right)\\ c.\left(x-1\right)\left(2x+1\right)+3\left(x-1\right)\left(x+2\right)\left(2x+1\right)\\ =\left(x-1\right)\left(2x+1\right)\left[1+3\left(x+2\right)\right]\\ =\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\\ d.\left(x-5\right)^2+\left(x+5\right)\left(x-5\right)-\left(5-x\right)\left(2x+1\right)\\ =\left(x-5\right)^2+\left(x+5\right)\left(x-5\right)+\left(x-5\right)\left(2x+1\right)\\ =\left(x-5\right)\left[\left(x-5\right)+\left(x+5\right)+\left(2x+1\right)\right]\\ =\left(x-5\right)\left(4x+1\right)\)
a) 3x2-3y2-2(x-y)2
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\\ =3\left(x+y\right)\left(x-y\right)-2\left(x-y\right)^2\\ =\left(x-y\right)\left(3-2x+2y\right)\)
a: \(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
b: Ta có: \(x^2-y^2-2x-2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
Phân tích đa thức sau thành nhân tử:
a) 14x2y - 21xy2 + 28x2y2
b) 3x2- 5x - 3xy + 5y
c) 5a3 - 20a
d) 2x+ 2y + x2+ 2xy + y2
a) \(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(2x-3y+4xy\right)\)
b) \(3x^2-5x-3xy+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
c) \(5a^3-20a\)
\(=5a\left(a^2-4\right)\)
\(=5a\left(a-2\right)\left(a+2\right)\)
d) \(2x+2y+x^2+2xy+y^2\)
\(=2\left(x+y\right)\left(x+y\right)^2\)
= \(=\left(x+y\right)\left(2+x+y\right)\)
phân tích đa thức sau thành phân tử
a) 3x4y - 12x2y3
b) x2 - y2 - 8y -16
c) x3 +3x2 + 4x +12
d) 3x2 - 6xy + 3y2 - 27
a) \(3x^4y-12x^2y^3=3x^2y\left(x^2-\left(2y\right)^2\right)=3x^2y\left(x+2y\right)\left(x-2y\right)\)
b) Sửa đề: \(x^2-y^2-8x+16=\left(x-4\right)^2-y^2=\left(x-4-y\right)\left(x-4+y\right)\)
c) \(x^3+3x^2+4x+12=x^2\left(x+3\right)+4\left(x+3\right)=\left(x^2+4\right)\left(x+3\right)\)
d) \(3x^2-6xy+3y^2-27=3\left(x^2-2xy+y^2-9\right)=3\left(\left(x-y^2\right)-3^2\right)=3\left(x-y-3\right)\left(x-y+3\right)\)
phân tích đa thức thành nhân tử
a/ x2 + 4x – 21
b/ 3x2 - 6xy + 3y2 – 3z2
c/ 2x2y + 12xy + 18y
a/ x2 + 4x - 21= x2 - 3x +4x - 21
= (x2+4x)-(3x+21)
= x(x+4)- 3(x+7)
= (x-3).(x+7)
b/ 3x2-6xy+3y2-3z2 = 3(x2- 2xy+y2- z2)
= 3[(x2 + 2xy + y2) – z2]
= 3[(x + y)2 – z2]
= 3(x + y – z)(x + y + z)
c/ 2x2y + 12xy + 18y = 2y(x2+6x+9)
Phân tích đa thức thành nhân tử:
a)4x3y2-8x2y+12xy2
b)3x2-6xy-5x+10y
c)x2-49+4y2-4xy
d)x2-6x-16
a) \(4x^3y^2-8x^2y+12xy^2=4xy\left(x^2y-2x+3y\right)\)
b) \(3x^2-6xy-5x+10y=3x\left(x-2y\right)-5\left(x-2y\right)=\left(x-2y\right)\left(3x-5\right)\)
c) \(x^2-49+4y^2-4xy=\left(x-2y\right)^2-49=\left(x-2y-7\right)\left(x-2y+7\right)\)
d) \(x^2-6x-16=\left(x^2-6x+9\right)-25=\left(x-3\right)^2-25=\left(x-3-5\right)\left(x-3+5\right)=\left(x-8\right)\left(x+2\right)\)
a) 4x3y2−8x2y+12xy2=4xy(x2y−2x+3y)4x3y2−8x2y+12xy2=4xy(x2y−2x+3y)
b) 3x2−6xy−5x+10y=3x(x−2y)−5(x−2y)=(x−2y)(3x−5)3x2−6xy−5x+10y=3x(x−2y)−5(x−2y)=(x−2y)(3x−5)
c) x2−49+4y2−4xy=(x−2y)2−49=(x−2y−7)(x−2y+7)x2−49+4y2−4xy=(x−2y)2−49=(x−2y−7)(x−2y+7)
d) x2−6x−16=(x2−6x+9)−25=(x−3)2−25=(x−3−5)(x−3+5)=(x−8)(x+2)
Phân tích đa thức thành nhân tử:
a)4x3y2-8x2y+12xy2
b)3x2-6xy-5x+10y
c)x2-49+4y2-4xy
d)x2-6x-16
a) \(4x^3y^2-8x^2y+12xy^2=4xy.x^2y-4xy.2x+4xy.3y=4xy\left(x^2y-2x+3y\right)\)
b) \(3x^2-6xy-5x+10y=\left(3x^2-6xy\right)-\left(5x-10y\right)=3x\left(x-2y\right)-5\left(x-2y\right)=\left(x-2y\right)\left(3x-5\right)\)
c) \(x^2-49+4y^2-4xy=\left(x^2-4xy+4y^2\right)-49=\left(x-2y\right)^2-7^2=\left(x-2y-7\right)\left(x-2y+7\right)\)
d) \(x^2-6x-16=\left(x^2-8x\right)+\left(2x-16\right)=x\left(x-8\right)+2\left(x-8\right)=\left(x-8\right)\left(x+2\right)\)