Phân tích đa thức thành nhân tử
a) 3x2 – 9x
b) 4x2 + 7y – 4xy – 7x
Phân Tích đa thức sau thành phân tử
a) 5x +10y
b)3x3 - 12x
c) 4x2+ 9x - 4xy -9y
d) 3x2+ 5y - 3xy - 5x
e)3y2 - 3z2 + 3x2 + xy
a) \(5x+10y=5\left(x+2y\right)\)
b) \(3x^3-12x=3x\left(x^2-4\right)=3x\left(x-2\right)\left(x+2\right)\)
c) \(4x^2+9x-4xy-9y=4x\left(x-y\right)+9\left(x-y\right)=\left(x-y\right)\left(4x+9\right)\)
d) \(3x^2+5y-3xy-5x=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
Phân tích đa thức sau thành nhân tử:
a) 4x2 + 4xy + y2 - 9
b) 3x2 - x - 3xy + y
a: \(=\left(2x+y\right)^2-3^2=\left(2x+y+3\right)\left(2x+y-3\right)\)
b: =3x(x-y)-(x-y)=(x-y)(3x-1)
Phân tích đa thức sau thành nhân tử: 4 x 2 - 4 x y
Phân tích đa thức thành nhân tử
A= x2+7x+7y-y2
B= 4x3-4x2+x
C= x2+9y2-9-6xy
\(A=x^2-y^2+7x+7y\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(B=4x^3-4x^2+x\)
\(=x\left(4x^2-4x+1\right)\)
\(=x\left(2x-1\right)^2\)
\(C=x^2-6xy+9y^2-9\)
\(=\left(x-3y\right)^2-9\)
\(=\left(x-3y-3\right)\left(x-3y+3\right)\)
A=\(x^2+7x+7y-y^2=\left(x^2-y^2\right)+\left(7x+7y\right)=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)=\left(x+y\right)\left(x-y+7\right)\)
B=\(4x^3-4x^2+x=x\left(4x^2-4x+1\right)=x\left(2x-1\right)^2\)
C=\(x^2+9y^2-9-6xy=\left(x^2-6xy+9y^2\right)-9=\left(x-3y\right)^2-3^2=\left(x-3y-3\right)\left(x-3y+3\right)\)
Phân tích đa thức thành nhân tử
a) 9x^3y^2-15x^2y^3
b) 25x^2-49y^2
c) x^2y-xy^2-7x+7y
PHÂN TÍCH CÁC ĐA THỨC SAU THÀNH NHÂN TỬ BẰNG PHƯƠNG PHÁP NHÓM NHIỀU HẠNG TỬ :
a) x2 -2x -4y2-4y
b) x4 + 2x3 - 4x -4
c) x3 + 2x2y -x -2y
d) 3x2 -3y2 -2(x-y)2
e) x3 -4x2 -9x +36
f) x2 -y2 -2x -2y
a: Ta có: \(x^2-4y^2-2x-4y\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
c: Ta có: \(x^3+2x^2y-x-2y\)
\(=x^2\left(x+2y\right)-\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-1\right)\left(x+1\right)\)
d: Ta có: \(3x^2-3y^2-2\cdot\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\cdot\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
e: Ta có: \(x^3-4x^2-9x+36\)
\(=x^2\left(x-4\right)-9\left(x-4\right)\)
\(=\left(x-4\right)\left(x-3\right)\left(x+3\right)\)
f: 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 thành nhân tử:
4x2- 4xy + y2 -8x +4y
2x3 - 3x2 + 3x -1
1)\(4x^2-4xy+y^2-8x+4y=\left(4x^2-4xy+y^2\right)-\left(8x-4y\right)=\left(2x-y\right)^2-4\left(2x-y\right)=\left(2x-y\right)\left(2x-y-4\right)\)
2) \(2x^3-3x^2+3x-1=x^2\left(2x-1\right)-x\left(2x-1\right)+\left(2x-1\right)=\left(2x-1\right)\left(x^2-x+1\right)\)
phân tích đa thức thành nhân tử (2x-y)(4x2-4xy+y2)-8x2(x-y)
\(\left(2x-y\right)\left(4x^2-4xy+y^2\right)-8x^2\left(x-y\right)\)
\(=\left(2x-y\right)^3-8x^2\left(x-y\right)\)
\(=8x^3-12x^2y+6xy^2-y^3-8x^3+8x^2y\)
\(=-4x^2y-6xy^2-y^3\)
\(=-y\left(4x^2+6xy+y^2\right)\)
Phân tích đa thức thành nhân tử:
a) x2-36y2-x+6y
b) 16x-8x2+x3
c) 2x2-4xy+2y2-18
d) 3x2-7x-10
e) x4-x2-30
f) x2-xy-2y2
g) x4-13x2y2+4y4
h) (x2-2x)2-2(x2-2x)-3
a) \(=\left(x+6y\right)\left(x-6y\right)-\left(x-6y\right)\)
\(=\left(x-6y\right)\left(x-6y-1\right)\)
b) \(=x\left(x^2-8x+16\right)\)
\(=x\left(x-4\right)^2\)
c) \(=2\left(x-y\right)^2-18\)
\(=2\left[\left(x-y\right)^2-3^2\right]\)
\(=2\left(x-y+3\right)\left(x-y-3\right)\)
a: \(x^2-36y^2-x+6y\)
\(=\left(x-6y\right)\left(x+6y\right)-\left(x-6y\right)\)
\(=\left(x-6y\right)\left(x+6y-1\right)\)
b: \(x^3-8x^2+16x\)
\(=x\left(x^2-8x+16\right)\)
\(=x\left(x-4\right)^2\)
c: \(2x^2-4xy+2y^2-18\)
\(=2\left(x^2-2xy+y^2-9\right)\)
\(=2\left(x-y-3\right)\left(x-y+3\right)\)
d: \(3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-10\right)\)
e: Ta có: \(x^4-x^2-30\)
\(=x^4-6x^2+5x^2-30\)
\(=x^2\left(x^2-6\right)+5\left(x^2-6\right)\)
\(=\left(x^2-6\right)\left(x^2+5\right)\)
f: Ta có: \(x^2-xy-2y^2\)
\(=x^2-2xy+xy-2y^2\)
\(=x\left(x-2y\right)+y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+y\right)\)
g: Ta có: \(x^4-13x^2y^2+4y^4\)
\(=x^4-4x^2y^2+4y^4-9x^2y^2\)
\(=\left(x^2-2y^2\right)^2-\left(3xy\right)^2\)
\(=\left(x^2-3xy-2y^2\right)\left(x^2+3xy-2y^2\right)\)