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Q
21 tháng 4 2017
a) \((2x^2−3x)(5x^2−2x+1)\)
\(=2x^2.5x^2−2x^2.2x+2x^2−3x.5x^2+3x.2x−3x\)
\(=10x^4−4x^3+2x^2−15x^3+6x^2−3x\)
\(=10x^4−19x^3+8x^2−3x\)
b) \((x−2y)(3xy+5y^2+x)\)
\(=x.3xy+x.5y^2+x.x−2y.3xy−2y.5y^2−2y.x\)
\(=3x^2y+5xy^2+x^2−6xy^2−10y^3−2xy\)
\(=3x^2y−xy^2−2xy+x^2−10y^3\)
S
21 tháng 12 2018
\(5x^3-5x=5x\left(x^2-1\right)\)
\(3x^2+5x-3xy-5x=x\left(3x+5\right)-x\left(3y+5\right)=x\left(3x-3y\right)=3x\left(x-y\right)\)
CS
28 tháng 10 2016
Làm tính nhân
(4x3+3xy2-2y3).(3x2-5xy-6y2)
=12x5+12y5-20x4y-36x2y3-8xy4
Phân tích đa thức thành nhân tử
10x3+5x2y-10x2y-10xy2+5y3
=10x3-5x2y-10xy2+5y3
=5(2x3-x2y-2xy2+y3-)
16 tháng 7 2017
a) \(x^4+2x^3+x^2=\left(x^2\right)^2+2.x^2.x+x^2=\left(x^2+x\right)^2\)
b) \(x^3-x+3x^2y+3xy^2+y^3-y=x^3+3x^2y+3xy^2+y^3-x-y\)
\(=\left(x-y\right)^3-\left(x+y\right)\)
c) \(5x^2-10xy+5y^2-20z^2=\left(\sqrt{5}x-\sqrt{5}y\right)^2-20z^2\)
4 tháng 9 2017
Câu b :
\(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
Câu c :
\(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2\right)-20z^2\)
\(=5\left(x-y\right)^2-20z^2\)
\(=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)
26 tháng 10 2019
1a) (x - 2y) (x2 - 2xy + y2)
= (x - 2y) (x - y)2
= x2 - xy - 2xy + 2y2
= (x2 - xy) - (2xy - 2y2)
= x (x - y) - 2y (x - y)
= (x - y) (x - 2y)
2a) x (x - 3) - y (3 - x)
= x (x - 3) + y (x - 3)
= (x - 3) (x + y)
b) 3x2 - 5x - 3xy + 5y
= (3x2 - 3xy) - (5x - 5y)
= 3x (x - y) - 5 (x - y)
= (x - y) (3x - 5)
3) 12x (3 - 4x) + 7 (4x - 3) = 0
12x (3 - 4x) - 7 (3 - 4x) = 0
(3 - 4x) (12x - 7) = 0
=> 3 - 4x = 0 hoặc 12x - 7 = 0
* 3 - 4x = 0 => x = \(\frac{3}{4}\)
* 12x - 7 = 0 => x = \(\frac{7}{12}\)
Vậy x =\(\frac{3}{4}\)hoặc x =\(\frac{7}{12}\)
PK
0
LT
19 tháng 4 2017
a) x2(5x3 – x - \(\dfrac{1}{2}\) )= x2. 5x3 + x2 . (-x) + x2 . (-\(\dfrac{1}{2}\))
= 5x5 – x3 – \(\dfrac{1}{2}\)x2
b) (3xy – x2 + y)\(\dfrac{2}{3}\)x2y = \(\dfrac{2}{3}\)x2y . 3xy + \(\dfrac{2}{3}\)x2y . (- x2) + \(\dfrac{2}{3}\)x2y . y
= 2x3y2 – \(\dfrac{2}{3}\)x4y + \(\dfrac{2}{3}\)x2y2
c) (4x3– 5xy + 2x)(- \(\dfrac{1}{2}\)xy) = - \(\dfrac{1}{2}\)xy . 4x3 + (- \(\dfrac{1}{2}\)xy) . (-5xy) + (- \(\dfrac{1}{2}\)xy) . 2x
= -2x4y + \(\dfrac{5}{2}\)x2y2 - x2y.
TT
14 tháng 8 2017
a) x2 (5x3 - x - \(\dfrac{1}{2}\))
= 5x5 - x3 - \(\dfrac{1}{2}\)x2
b) (3xy - x2 + y) \(\dfrac{2}{3}\)x2y
= 2x3y2 - \(\dfrac{2}{3}\)x4y + \(\dfrac{2}{3}\)x2y2
c) (4x3 - 5xy +2x) (-\(\dfrac{1}{2}\)xy)
= -2x4y + \(\dfrac{5}{2}\)x2y2 - x2y
9 tháng 12 2018
1)\(x^2-y^2+2x-4y-10=0\)
\(\Leftrightarrow\left(x^2+2x+1\right)-\left(y^2+4y+4\right)-7=0\)
\(\Leftrightarrow\left(x+1\right)^2-\left(y+2\right)^2=7\)
\(\Leftrightarrow\left(x+1-y-2\right)\left(x+1+y+2\right)=7\)
\(\Leftrightarrow\left(x-y-1\right)\left(x+y+3\right)=7\)
Xét ước
2) \(x^2+2y^2+3xy+3x+3y=15\)
\(\Leftrightarrow x^2+y^2+2xy+y^2+xy+3x+3y=15\)
\(\Leftrightarrow\left(x+y\right)^2+y\left(x+y\right)+3\left(x+y\right)=15\)
\(\Leftrightarrow\left(x+y\right)\left(x+2y+3\right)=15\)
Xét ước
\(2x^2+3xy-2y^2=7\)
\(\Leftrightarrow2x^2+4xy-2y^2-xy=7\)
\(\Leftrightarrow2x\left(x+2y\right)-y\left(x+2y\right)=7\)
\(\Leftrightarrow\left(2x-y\right)\left(x+2y\right)=7\)
Xét ước
20 tháng 4 2017
Bài giải:
a) (-2x5 + 3x2 – 4x3) : 2x2 = (- 2222)x5 – 2 + 3232x2 – 2 + (-4242)x3 – 2 = - x3 + 3232 – 2x.
b) (x3 – 2x2y + 3xy2) : (- 1212x) = (x3 : -1212x) + (-2x2y : -1212x) + (3xy2 : -1212x)
= -2x2 + 4xy – 6y2
c)(3x2y2 + 6x2y3 – 12xy) : 3xy = (3x2y2 : 3xy) + (6x2y2 : 3xy) + (-12xy : 3xy)
= xy + 2xy2 – 4.
20 tháng 4 2017
a) (-2x5+3x2-4x3) : 2x2
= (-2x5:2x2)-(4x3:2x2)+(3x2:2x2)
= -x3-2x+\(\dfrac{3}{2}\)
b) \(\left(x^3-2x^2y+3xy^2\right):\left(-\dfrac{1}{2}x\right)\)
= \(\left(x^3:\dfrac{-1}{2}x\right)+\left(-2x^2y:\dfrac{-1}{2}x\right)+\left(3xy^2:\dfrac{-1}{2}x\right)\)
= \(-2x^2+4xy-6y^2\)
c) \(\left(3x^2y^2+6x^2y^3-12xy\right):3xy\)
= \(\left(6x^2y^3:3xy\right)+\left(3x^2y^2:3xy\right)+\left(-12xy:3xy\right)\)
= \(xy^2+xy-4\)
WI
1
10 tháng 7 2018
a) 5x - 5y + ax - ay = 5(x - y) + a(x - y)
= (5 + a)(x - y)
b) x3 - x + 3x2y + 3xy2 + y3 - y
= (x3 + 3x2y + 3xy2 + y3) - (x + y)
= (x + y)3 - (x + y)
= (x + y)[(x + y)2 - 1]
= (x + y)(x + y + 1)(x + y - 1)
c) x2 - 2x - 3 = x2 + x - 3x -3
= x(x + 1) - 3(x + 1)
= (x - 3)(x + 1)
e) 6x - 9 - x2 = 3x - 9 + 3x - x2
= 3(x - 3) + x(3 - x)
= 3(x - 3) - x(x - 3)
= (3 - x)(x - 3)
(x – 2y)(3xy + 5y2 + x)
= x.(3xy + 5y2 + x) + (-2y).(3xy + 5y2 + x)
= x.3xy + x.5y2 + x.x + (-2y).3xy + (–2y).5y2 + (–2y).x
= 3x2y + 5xy2 + x2 – 6xy2 – 10y3 – 2xy
= 3x2y + (5xy2 – 6xy2) + x2 – 10y3 – 2xy
= 3x2y – xy2 + x2 – 10y3 – 2xy