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24 tháng 7 2016
1) x(x - y) + x - y
= x.(x - y) + (x - y)
= (x - y).(x + 1)
2) Câu b sai đề nên mk sửa lại nha
2x3 + x2 - 8x - 4
= (2x3 + x2) - (8x + 4)
= x2.(2x + 1) - 4.(2x + 1)
= (2x + 1).(x2 - 4)
= (2x + 1).(x - 2).(x + 2)
3) 2x2 - 8xy - 5x + 20y
= (2x2 - 5x) - (8xy - 20y)
= x.(2x - 5) - 4y.(2x - 5)
= (2x - 5).(x - 4y)
KL
24 tháng 7 2016
1) ( x+1) ( x-y)
2) 2x3 + x2 - 8x - 4= 2x3 - 4x2 + 5x2 - 10x + 2x - 4 = 2x2 ( x-2) + 5x( x -2) + 2(x -2)
=( 2x2 + 5x + 2)( x-2)
=( 2x2 + 4x + x + 2)( x-2)
=[ 2x( x+2) + ( x-2)]( x-2)
= ( 2x +1)( x+2)( x-2)
3) 2x2 - 8xy - 5x + 20y
= 2x ( x - 4y) - 5( x-4y)= ( 2x-5)(x-4y)
16 tháng 8 2020
a) Ta có: \(x^2-2xy+y^2-4\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
b) Ta có: \(-16x^2+8xy-y^2+49\)
\(=-\left(16x^2-8xy+y^2-49\right)\)
\(=-\left[\left(16x^2-8xy+y^2\right)-49\right]\)
\(=-\left[\left(4x-y\right)^2-7^2\right]\)
\(=-\left(4x-y-7\right)\left(4x-y+7\right)\)
c) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
\(=\left(x+1\right)\left(x^5-x^4+2x^2\right)\)
\(=\left(x+1\right)\left[\left(x^5+x^2\right)-\left(x^4-x^2\right)\right]\)
\(=\left(x+1\right)\left[x^2\left(x^3+1\right)-x^2\left(x^2-1\right)\right]\)
\(=x^2\cdot\left(x+1\right)\cdot\left(x^3+1-x^2+1\right)\)
\(=x^2\cdot\left(x+1\right)\cdot\left(x^3-x^2+2\right)\)
d) Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\cdot\left(3x^2+y^2\right)\)
8 tháng 10 2017
\(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x-y\right)^2-4\left(4x-y\right)\)
\(=\left(4x-y\right)\left(4x-y-4\right)\)
8 tháng 10 2017
a) \(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x\right)^2-8xy+y^2+4\left(y-4x\right)\)
\(=\left(4x-y\right)^2+4\left(y-4x\right)\)
\(=\left(y-4x\right)^2+4\left(y-4x\right)=\left(y-4x\right)\left(y-4x+4\right)\)
AT
17 tháng 6 2017
a/ \(3x^2\left(4x^3-2x+\dfrac{1}{3}\right)=12x^5-6x^3+x^2\)
b/ \(\left(4x^2+8xy-3xy^2\right)\left(-\dfrac{3}{4}x^2y\right)\)
\(=-3x^4y-6x^3y^2+\dfrac{9}{4}x^3y^3\)
c/ \(4x^3\left(2x^2-x+5\right)5x=20x^4\left(2x^2-x+5\right)\)
\(=40x^6-20x^5+100x^4\)
DH
17 tháng 6 2017
a, \(3x^2\left(4x^3-2x+\dfrac{1}{3}\right)\)
\(=12x^5-6x^3+x^2\)
b, \(\left(4x^2+8xy-3xy^2\right).\left(\dfrac{-3}{4}x^2y\right)\)
\(=-3x^4y-6x^3y^2+\dfrac{9}{4}x^3y^3\)
c, \(4x^3\left(2x^2-x+5\right)5x\)
\(=\left(8x^5-4x^4+20x^3\right)5x\)
\(=40x^6-20x^5+100x^4=20x^4.\left(2x^2-x+5\right)\)
Chúc bạn học tốt!!! Mình không chắc đâu !
28 tháng 5 2022
a: \(2.5x^4+0.75x^3-0.2x^2\)
\(=x^2\left(2.5x^2+0.75x-0.2\right)\)
b: \(7x^5y-\dfrac{3}{4}x^4y^2+\dfrac{1}{2}x^3y^3-3xy^5\)
\(=xy\left(7x^4-\dfrac{3}{4}x^3y+\dfrac{1}{2}x^2y^2-3y^4\right)\)
c: \(=y^2z\left(12x^2-8z-0.1z^2\right)\)
10 tháng 4 2020
a)
\(12xy-4x^2y+8xy^2\\ =4xy\cdot\left(3-x+2y\right)\)
b)
\(4x\cdot\left(x-2y\right)-8y\cdot\left(x-2y\right)\\ =4\cdot\left(x-2y\right)\cdot\left(x-2y\right)\\ =4\cdot\left(x-2y\right)^2\)
c)
\(25x^2\cdot\left(y-1\right)-5x^3\cdot\left(1-y\right)\\ =-25x^2\cdot\left(1-y\right)-5x^3\cdot\left(1-y\right)\\ =\left(1-y\right)\cdot\left(-25x^2-5x^3\right)\\ =5x^2\left(1-y\right)\cdot\left(-5-x\right)\)
d)
\(3x\cdot\left(a-x\right)+4a\cdot\left(a-x\right)\\ =\left(a-x\right)\cdot\left(3x+4a\right)\)
e)
\(x^3-3x^2+2\\ =x^3-x^2-2x^2+2\\ =x^2\cdot\left(x-1\right)-2\left(x^2-1\right)\\ =x^2\cdot\left(x-1\right)-2\cdot\left(x-1\right)\cdot\left(x+1\right)\\ =\left(x-1\right)\left[x^2-2\cdot\left(x+1\right)\right]\\ =\left(x-1\right)\cdot-\left(x^2+2x+1\right)\\ =\left(x-1\right)\cdot-\left(x+1\right)^2\)
TG
3 tháng 9 2020
a) \(\left(3x^2y-11x^2-5y\right)\left(8xy-5x+6\right)\)
\(=3x^2y\left(8xy-5x+6\right)-11x^2\left(8xy-5x+6\right)-5y\left(8xy-5x+6\right)\)
\(=24x^3y^2-15x^3y+18x^2y-88x^3y+55x^3-66x^2-40xy^2+25xy-30y\)
\(=24x^3y^2-103x^3y+18x^2y+55x^3-66x^2-40xy^2+25xy-30y\)
b) \(\left(-4x^2y-5x^2+3y^3\right)\left(2x^2-xy+3y^2\right)\)
\(=-4x^2y\left(2x^2-xy+3y^2\right)-5x^2\left(2x^2-xy+3y^2\right)+3y^3\left(2x^2-xy+3y^2\right)\)
\(=-8x^4y+4x^3y^2-12x^2y^3-10x^4+5x^3y-15x^2y^2+6x^2y^3-3xy^4+9y^5\)
\(=-8x^4y+4x^3y^2-6x^2y^3-10x^4+5x^3y-15x^2y^2-3xy^4+9y^5\)
P/s: Ko chắc ạ!
8 tháng 10 2017
a) 16x2 + y2 + 4y - 16x - 8xy = ( 16x2 - 8xy + y2 ) - ( 16x - 4y )
= ( 4x - y )2 - 4 . ( 4x - y )
= ( 4x - y ) . ( 4x - y - 4 )
TH
28 tháng 12 2016
a) \(2x^2\left\{x^2+5x+6\right\}\)=\(2x^4+10x^3+12x^2\)
b) \(15x^2y^4:10x^2y\)=\(\frac{3}{2}y^3\)
c) \(\left\{16x^3y^2+20x^2y^3-8xy\right\}:4xy\)=\(4x^2y+5xy^2-2\)
\(2x^3y-8xy^3=2xy\left(x^2-4y^2\right)=2xy\left(x-2y\right)\left(x+2y\right)\)