Phân tích đa thức thành nhân tử:
1) x^2+x-xy-2y^2+y
2) 6x^2+xy-7x-2y^2+7y-5
3) 6a^2-ab-2b^2+a+4b-2
4) 3x^2-22xy-4x+8y+7y^2+1
5) 2x^2+5x-12y^2+12y-3-10x
Cảm ơn
Phân tích thành nhân tử ( tách các hạng tử)
1,x^2-6x+3
2, 2m^2+10m+8
3, 9x^2+6x-8
4, x^3-5x^2-14x
5, a^4+4a^2-5
6, x^3-7x-6
7, 3x^2-22xy+4x+8y+7y^2+1
8, 12x^2+5x-12y^2+12y-10xy-3
1) \(x^2-6x+3\)
\(=x^2-6x+9-6\)
\(=\left(x-3\right)^2-6\)
\(=\left(x-3+\sqrt{6}\right)\left(x-3-\sqrt{6}\right)\)
2) \(2m^2+10m+8\)
\(=2m^2+2m+8m+8\)
\(=2m\left(m+1\right)+8\left(m+1\right)\)
\(=\left(2m+8\right)\left(m+1\right)\)
\(=2\left(m+4\right)\left(m+1\right)\)
3) \(9x^2+6x-8\)
\(=\left(9x^2+6x+1\right)-9\)
\(=\left(3x+1\right)^2-9\)
\(=\left(3x+4\right)\left(3x-2\right)\)
4) \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2-2x+7x-14\right)\)
\(=x\left[x\left(x-2\right)+7\left(x-2\right)\right]\)
\(=x\left(x+7\right)\left(x-2\right)\)
1) x^2-6x+3
= (x^2-6x+9)-6
=(x-3)^2-6
=(x-3-căn 6)(x-3+căn 6)
2) =2(m^2+5m+4)
=2(m+1)(m+4)
3) =9x^2+6x+1-9
=(3x+1)^-9
=(3x-2)(3x+4)
4, x^3-5x^2-14x
=x(x-7)(x+2)
5, a^4+4a^2-5
=a^4+4a^2+4-9
=(a^2+2)^-9
=(a^2-1)(a^2+5)
6, x^3-7x-6
=(x-3)(x+1)(x+2).
5) \(a^4+4a^2-5\)
\(=a^4+5a^2-a^2-5\)
\(=a^2\left(a^2+5\right)-\left(a^2+5\right)\)
\(=\left(a^2-1\right)\left(a^2+5\right)\)
\(=\left(a+1\right)\left(a-1\right)\left(a^2+5\right)\)
6) \(x^3-7x-6\)
\(=x^3-x-6x-6\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)
Phân tích đa thức thành nhân tử:
1, (x+y)^7-x^7-y^7
2, x^4+4x^2+5
3, x^2+2xy-8y^2+2xz+14yz-3z^2
4, 3x^2-22xy-4x+8y+7y^2+1
5, 12x^2+5x-12y^2+12y-10xy-3
6, 2x^2-7xy+3y^2+5xz-5yz+2z^2
7, x^2+3xy+2y^2+3xz+5yz+2z^2
8, x^2-8xy+15y^2+2x-4y-3
phân tích thành nhân tử bằng hệ số bất định
a,3x^2−22xy−4x+8y+7y^2+1
b,12x^2+5x−12y^2+12y−10xy−3
c,x^4+6x^3+11x^2+6x+1
Phân tích đa thức thành nhân tử
1) 32X^4+1
2)X^8+3x^4+1
3)x^2+2xy-8y^2+2xz+14yz-3z^2
4)3x^2-22xy-4x+8y+7y^2+1
5)12x^2+5x-12y^2+12y-10xy-3
6)2x^2-7xy+3y^2+5xz-5yz+2z^2
7)x^2+3xy+2y^2+3xz+5yz=2z^2
8)x^2-8xy+15y^2+2x-4y-3
9)x^4-13x^2+36
10)4(x^2+15x+50)(x^2+18x+72)-3x^2
Phân tích đa thức thành nhân tử
5x^2y - 10x^2y^2 + 5xy^3
4x^3 - 36
X^2 - 4
X^2 - 6x + 9
27 + 27x + 9x ^2 +x^3
X^2 - 25 -2 xy +y^2
7y^4 - 14y^3 + 7y^2
1 - 4x^2
3x + 9 + 4x^2 + 12x
(X + 1 )^2 - 25
X^2 - y^2 + 4x +4
6x^2 + 6xy - 7x - 7y
Phân tích thành nhân tử
a,3x2-22xy-4x+8y+7y2+1
b,12x2+5x-12y2+12y-10xy-3
c,x4+6x3+11x2+6x+1
c, x4+6x3+11x2+6x+1
=x4+6x3+9x2+2x2+6x+1
=x4+9x2+1+6x3+2x2+6x
=(x2)2+(3x)2+12+2.x2.3x+2.x2.1+2.3x.1 (1)
Áp dụng hằng đẳng thức (a+b+c)2=a2+b2+c2+2ab+2ac+2bc
=> (1)=(x2+3x+1)2
Câu a nhé bạn:
a, 3x2−22xy−4x+8y+7y2+1
=3x2-21xy-xy-3x-x+7y+y+7y2+1
=(3x2−21xy−3x)−(xy-7y2-y)−(x-7y-1)
=3x(x−7y−1)−y(x−7y−1)−(x−7y−1)
=(3x−y−1)(x−7y−1)
Cho mk hs bn Diệu Thúy để lm đc như câu a) thì có pp j k bn? Hay chỉ lag ngồi nhóm lại thôi hả bn? Trả lời nhanh dùm mk nha😘
phân tích đa thức thành nhân tử bằng kỹ thuật tách hạng tử:
1. 3x2+8xy-3y2
2. x2+2y2-3xy+x+2y
3 x2-4xy-x+3y2+3y
4. 6x2+xy-7x-2y2+7y-5
5. 3x2-22xy-4x+8y+7y2+1
6. 2a2 +5ab-3b2-7b-2
7. 6x2-xy-2y2+3x-2y
8. 2x2-3xy-4x-9y2-6y
Làm giúp mình với ,nhớ ghi số câu ,cảm ơn nhìu
Phân tích thành nhân tử bằng kĩ thuật bổ sung hằng đẳng thức
x^2-4xy-x+3y^2+3y
x^2+4xy+2x+3y^2+6y
6x^2+xy-7x-2y^2+7y-5
6a^2-ab-2b^2+a+4b
phân tích đa thức thành nhân tử
\(a)3x^3+6x^2y \)
\(b)2x^3-6x^2\)
\(c)18x^2-20xy\)
\(d)xy+y^2-x-y \)
\(e)(x^2y^2-8)^2-1\)
\(f)x^2-7x-8\)
\(g)10x^2(2x-y)+6xy(y-2x)\)
\(h)x^2-2x+1-y^2\)
\(i)2x(x+2)+x^2(-x-2)\)
\(k)-9+6x-x^2\)
\(l)8xy-2x^2-8y^2\)
\(m)3x^2+5x-3y^2-5y\)
a) 3x³ + 6x²y
= 3x².(x + 2y)
b) 2x³ - 6x²
= 2x².(x - 2)
c) 18x² - 20xy
= 2x.(9x - 10y)
d) xy + y² - x - y
= (xy + y²) - (x + y)
= y(x + y) - (x + y)
= (x + y)(y - 1)
e) (x²y² - 8)² - 1
= (x²y² - 8 - 1)(x²y² - 8 + 1)
= (x²y² - 9)(x²y² - 7)
= (xy - 3)(xy + 3)(x²y² - 7)
f) x² - 7x - 8
= x² - 8x + x - 8
= (x² - 8x) + (x - 8)
= x(x - 8) + (x - 8)
= (x - 8)(x + 1)
a: \(3x^3+6x^2y\)
\(=3x^2\cdot x+3x^2\cdot2y=3x^2\left(x+2y\right)\)
b: \(2x^3-6x^2=2x^2\cdot x-2x^2\cdot3=2x^2\left(x-3\right)\)
c: \(18x^2-20xy=2x\cdot9x-2x\cdot10y=2x\left(9x-10y\right)\)
d: \(xy+y^2-x-y\)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(y-1\right)\)
e: \(\left(x^2y^2-8\right)^2-1\)
\(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)
\(=\left(x^2y^2-7\right)\left(x^2y^2-9\right)\)
\(=\left(x^2y^2-7\right)\left(xy-3\right)\left(xy+3\right)\)
f: \(x^2-7x-8\)
\(=x^2-8x+x-8\)
\(=x\left(x-8\right)+\left(x-8\right)=\left(x-8\right)\left(x+1\right)\)
g: \(10x^2\left(2x-y\right)+6xy\left(y-2x\right)\)
\(=2x\cdot\left(2x-y\right)\cdot5x-2x\cdot\left(2x-y\right)\cdot3y\)
\(=2x\left(2x-y\right)\left(5x-3y\right)\)
h: \(x^2-2x+1-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1-y\right)\left(x-1+y\right)\)
i: \(2x\left(x+2\right)+x^2\left(-x-2\right)\)
\(=2x\left(x+2\right)-x^2\left(x+2\right)\)
\(=\left(x+2\right)\left(2x-x^2\right)=x\cdot\left(x+2\right)\left(2-x\right)\)
k: \(-x^2+6x-9=-\left(x^2-6x+9\right)\)
\(=-\left(x^2-2\cdot x\cdot3+3^2\right)=-\left(x-3\right)^2\)
l: \(-2x^2+8xy-8y^2\)
\(=-2\left(x^2-4xy+4y^2\right)\)
\(=-2\left(x-2y\right)^2\)
m: \(3x^2+5x-3y^2-5y\)
\(=3\left(x^2-y^2\right)+5\left(x-y\right)\)
\(=3\left(x-y\right)\left(x+y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+3y+5\right)\)
g) 10x²(2x - y) + 6xy(y - 2x)
= 10x²(2x - y) - 6xy(2x - y)
= 2x(2x - y)(5x - 3y)
h) x² - 2x + 1 - y²
= (x² - 2x + 1) - y²
= (x - 1)² - y²
= (x - y - 1)(x + y - 1)
i) 2x(x + 2) + x² (-x - 2)
= 2x(x + 2) - x²(x + 2)
= x(x + 2)(2 - x)
k) -9 + 6x - x²
= -(x² - 6x + 9)
= -(x - 3)²
l) 8xy - 2x² - 8y²
= -2(x² - 4xy + 4y²)
= -2(x - 2y)²
m) 3x² + 5x - 3y² - 5y
= (3x² - 3y²) + (5x - 5y)
= 3(x² - y²) + 5(x - y)
= 3(x - y)(x + y) + 5(x - y)
= (x - y)[3(x + y) + 5]
= (x - y)(3x + 3y + 5)