x2-xy+y2
đa thức thành nhân tử
Phân tích đa thức thành nhân tử
a/ 3x2 – 30x +75
b/ x2 +xy +8x +8y
c/ x2 +4x +4 - y2
a) \(=3\left(x^2-10x+25\right)=3\left(x-5\right)^2\)
b) \(=x\left(x+y\right)+8\left(x+y\right)=\left(x+y\right)\left(x+8\right)\)
c) \(=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
a) =3(x2−10x+25)=3(x−5)2
b) =x(x+y)+8(x+y)=(x+y)(x+8)
c) =(x+2)2−y2=(x+2−y)(x+2+y)
Phân tích đa thức thành nhân tử (bằng phương pháp nhóm hạng tử)
c/ 5x2 + 3y + 15x + xy d/ x2 + 6x + 9 – y2
e/ x2 – y2 + 2x + 1 f/ x2 – 2xy – 9 + y2
c) \(5x^2+3y+15x+xy=5x\left(x+3\right)+y\left(x+3\right)=\left(x+3\right)\left(5x+y\right)\)
d) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+3-y\right)\left(x+3+y\right)\)
e) \(x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
f) \(x^2-2xy-9+y^2=\left(x^2-2xy+y^2\right)-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
c: \(5x^2+15x+3y+xy\)
\(=5x\left(x+3\right)+y\left(x+3\right)\)
\(=\left(x+3\right)\left(5x+y\right)\)
d: \(x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
e: \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1-y\right)\left(x+1+y\right)\)
f: \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-9\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
Phân tích đa thức thành nhân tử:
x2 + y2 - x2y2 + xy - x - y
x2 + y2 - x2y2 + xy - x - y = (x2-x) + (y2-y) + (-x2y2 + xy) = x(x+1) + y(y+1) + xy(xy+1) = ( x+ y+ xy)( x + 1 + y + 1 + xy + 1)
\(x^2+y^2-x^2y^2+xy-x-y\)
\(=\left(x^2-x\right)+\left(y^2-y\right)+ \left(-x^2y^2+xy\right)\)
\(=x\left(x+1\right)+y\left(y+1\right)+xy\left(xy+1\right)\)
\(=\left(x+y+xy\right)\left(x+1+y+1+xy+1\right)\)
Phân tích đa thức thành nhân tử: (Giup e vs nhaaa)
a) 4xy - 20x3y2
b) x2 - y2 + 3x - 3y
c) x2 - ax + xy - ay
d) x2 - 36 + 4xy + 4y2
a: \(=4xy\left(1-5x^2y\right)\)
b: \(=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\)
c: \(=x\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(x+y\right)\)
d: \(=\left(x+2y\right)^2-36=\left(x+2y+6\right)\left(x+2y-6\right)\)
Phân tích các đa thức sau thành nhân tử
a) x 2 + x y − 5 x − 5 y
b) 25 − x 2 − y 2 − 2 x y
c) x 4 + x 3 + 2 x 2 + x + 1
Phân tích các đa thức sau thành nhân tử:
a) x 2 + 6x + 8; b) 2 x 2 + 14x +12;
c) 9 x 2 + 24x +15; d) 6 x 2 -xy-7 y 2 .
a) (x + 2)(x + 4). b) 2(x + 6)(x + l).
c) 3(3x + 5)(x + l). d) (6x -7y)(x + y).
phân tích các đa thức sau thành nhân tử
a) 5x2 - 10xy + 5y2 - 20z
b) x2 - z2 + y2 - 2xy
c) a3 - ay - a2x + xy
d) x2 + 4x + 3
b: \(x^2-2xy+y^2-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
d: \(x^2+4x+3=\left(x+3\right)\left(x+1\right)\)
=x4−2x3+2x3−4x2+4x2−8x+7x−14=x4−2x3+2x3−4x2+4x2−8x+7x−14
=(x−2)(x3+2x2+4x+7)
Bài 2 Phân tích đa thức sau thành nhân tử
a. x4 + 2x3 − 4x − 4
b. x2(1 − x2) − 4 − 4x2
c. x2 + y2 − x2y2 + xy − x − y
d* a3 + b3 + c3 − 3abc
a) \(x^4+2x^3-4x-4=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
a) Ta có: \(x^4+2x^3-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\cdot\left(x^2+2x+2\right)\)
d) Ta có: \(a^3+b^3+c^3-3abc\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)
\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)
Phân tích đa thức thành nhân tử:
a) 2 x 3 - x 2 - 8x + 4; b) 4 x 2 - 16 x 2 y 2 + y 2 + 4xy;
c) x 3 - 16x - 15x(x - 4); d) x ( x - y ) 2 + y ( x - y ) 2 - xy + x 2 .
Bài 2:Phân tích đa thức thành nhân tử chung
a, 4(2-x)2+xy-2y
b, x(x-y)3-y(y-x)2-y2(x-y)
c, x2y-xy2-3x+3y
d, x(x+y)2-y(x+y2)+xy-x2
a) \(4\left(2-x\right)^2+xy-2y\)
\(=4\left(x-2\right)^2+\left(xy-2y\right)\)
\(=4\left(x-2\right)\left(x-2\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8+x-2\right)\)
\(=\left(x-2\right)\left(5x-10\right)\)
\(=5\left(x-2\right)^2\)
a, \(=4\left(x-2\right)^2+y\left(x-2\right)=\left(x-2\right)\left(4x-8+y\right)\)
b, \(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-xy+y^2-y^2\right]=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)=x\left(x-y\right)\left(x^2-2xy+y^2-y\right)\)
c, \(=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\)
d, không phân tích được
c, x2y - xy2 - 3x + 3y
= xy(x-y) - 3(x-y)
= (x-y)(x-3)