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
K
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KN
13 tháng 11 2019
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) \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2-2x+7x-14\right)\)
\(=x\left[x\left(x-2\right)+7\left(x-2\right)\right]\)
\(=x\left(x+7\right)\left(x-2\right)\)
2 tháng 8 2016
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
2 tháng 8 2016
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)
KV
30 tháng 10 2023
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)
30 tháng 10 2023
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: \(3x^2+5x-3y^2-5y\)
\(=3\left(x^2-y^2\right)+5\left(x-y\right)\)
\(=3\left(x-y\right)\left(x+y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+3y+5\right)\)
1/\(x^2+x-xy-2y^2+y\)
=\(x\left(x+1-y\right)-y\left(x+2y-1\right)\)