Phân tích thành nhâ tử
a, \(-x^2-2x+15\)
b,\(2x^2-xy-y^2\)
c,\(16x^4+1\)
d, \(-6x^2-5y+3xy+10x\)
trình bày cách làm nữa nha
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![](https://rs.olm.vn/images/avt/0.png?1311)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
![](https://rs.olm.vn/images/avt/0.png?1311)
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: \(3x^2+5x-3y^2-5y\)
\(=3\left(x^2-y^2\right)+5\left(x-y\right)\)
\(=3\left(x-y\right)\left(x+y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+3y+5\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b)x2+2xy+y2-16=(x+y)2-42=(x+y+4)(x+y-4)
c)3x2+5x-3xy-5y=x(3x+5)-y(3x+5)=(3x+5)(x-y)
d)4x2-6x3y-2x2+8x=2x(2x-3x2y-x+4)
e)x2-4-2xy+y2=(x2-2xy+y2)-4=(x-y)2-22=(x-y-2)(x-y+2)
k)x2-y2-z2-2yz=x2-(y+z)2=(x-y-z)(x+y+z)
m)6xy+5x-5y-3x2-3y2=3(x2-2xy+y2)+5(x-y)=3(x-y)2+5(x-y)=(x-y)(3x-3y+5)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5+y\right)\left(x+5-y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(x^2+2\right)\left(5x-7\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5-y\right)\left(x+5+y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(5x-7\right)\left(x^2+2\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
dài quá mình làm 3 câu đầu thôi nhé!
a)7x^2-14xy
=7x(x-2y)
b) 3x^2-6xy+3y^2
=3(x^2-2xy+y^2)
c) x^2-4z^2-2xy+y^2
=(x^2-2xy+y^2)-4z^2
=(x-y-2z)(x-y+2z)
=3(x-y)^2
c)
a) (-x+5)(x+3)
b) x2-y2+x2-xy
(x-y)(x+y)+x(x-y)
(x-y)(2x+y)
d) 10x-6x2-5y+3xy
2x(5-3x)-y(5-3x)
(2x-y)(5-3x)
thông cảm câu c hok bít làm câu a bạn nhân ra là bạn thấy