x2y-xy2-7x+7y
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NN
1
25 tháng 12 2021
\(=xy\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(xy-7\right)\)
10 tháng 3 2022
a: \(=3x^4+3x^2y^2+2x^2y^2+2y^4+y^2\)
\(=\left(x^2+y^2\right)\left(3x^2+2y^2\right)+y^2\)
\(=3x^2+3y^2=3\)
b: \(=7\left(x-y\right)+4a\left(x-y\right)-5=-5\)
c: \(=\left(x-y\right)\left(x^2+xy+y^2\right)+xy\left(y-x\right)+3=3\)
d: \(=\left(x+y\right)^2-4\left(x+y\right)+1\)
=9-12+1
=-2
10 tháng 10 2021
a) \(=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
\(=\left(x-1\right)^2\left(x^2+x+1\right)\)
b) \(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
c) Đổi đề: \(a^2x+a^2y-7x-7y\)
\(=a^2\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(a^2-7\right)\)
d) \(=x^2\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x^2+y\right)\)
e) \(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
g) \(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h) \(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)
i) \(=\left(x+1\right)^2-4=\left(x+1-2\right)\left(x+1+2\right)=\left(x-1\right)\left(x+3\right)\)
10 tháng 10 2021
a\(x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
b)\(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
d)\(=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(x^2+y\right)\left(x-b\right)\)
e)\(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
g)\(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h)\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)
i)\(=\left(x-1\right)^2-4=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\)
CM
5 tháng 6 2019
Ta có A + 2B = (x2y - xy2 + 3x2) + 2(x2y + xy2 - 2x2 - 1)
= x2y - xy2 + 3x2 + 2x2y + 2xy2 - 4x2 - 2
= 3x2y + xy2 - x2 - 2. Chọn C
NH
2
27 tháng 8 2021
\(x^3-x^2y+7x-7y=\left(x^3-x^2y\right)+\left(7x-7y\right)=x^2\left(x-y\right)+7\left(x-y\right)=\left(x-y\right)\left(x^2+7\right)\)
27 tháng 8 2021
\(x^3-x^2y+7x-7y\)
\(=x^2\left(x-y\right)+7\left(x-y\right)\)
\(=\left(x-y\right)\cdot\left(x^2+7\right)\)
9 tháng 1 2023
a: \(\dfrac{\left(x+1\right)}{x^2+2x-3}=\dfrac{\left(x+1\right)}{\left(x+3\right)\cdot\left(x-1\right)}=\dfrac{\left(x+1\right)\left(x+2\right)\left(x+5\right)}{\left(x+3\right)\left(x-1\right)\left(x+2\right)\left(x+5\right)}\)
\(\dfrac{-2x}{x^2+7x+10}=\dfrac{-2x}{\left(x+2\right)\left(x+5\right)}=\dfrac{-2x\left(x+3\right)\left(x-1\right)}{\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x-1\right)}\)
b: \(\dfrac{x-y}{x^2+xy}=\dfrac{x-y}{x\left(x+y\right)}=\dfrac{y^2\left(x-y\right)}{xy^2\left(x+y\right)}\)
\(\dfrac{2x-3y}{xy^2}=\dfrac{\left(2x-3y\right)\left(x+y\right)}{xy^2\left(x+y\right)}\)
c: \(\dfrac{x-2y}{2}=\dfrac{\left(x-2y\right)\left(x-xy\right)}{2\left(x-xy\right)}\)
\(\dfrac{x^2+y^2}{2x-2xy}=\dfrac{x^2+y^2}{2\left(x-xy\right)}\)
20 tháng 6 2021
a/ 5x2y (x2y– 4xy2 + 7xy)
`=5x^4y^2-20x^3y^3+35x^3y^2`
b/ 3xy2 (x2y3 + x 2y – xy2 )
`=3x^3y^5+3x^3y^3-3x^2y^4`
c/ 3x(12x2 + 4x – 5) + 2x(9x2 – 6x + 7)
`=36x^3+12x^2-15x+18x^3-18x^2+14x`
`=54x^3-6x^2-x`
d/ 5x(2x2 – 9x – 5) – 9x (x2 - 7x – 4)
`=10x^3-45x^2-25x-9x^3+63x^2+36x`
`=x^3+18x^2+11x`
26 tháng 11 2023
a: \(70a+84b-20ab-24b^2\)
\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)
\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)
\(=\left(5a+6b\right)\left(14-4b\right)\)
\(=2\left(7-2b\right)\left(5a+6b\right)\)
b: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2\right)+\left(y^2z+yz^2\right)+3xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+3xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+2xyz+xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z+x\right)\)
\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z+x\right)\)
\(=\left(y+z\right)\cdot x\left(x+y+z\right)+yz\left(y+z+x\right)\)
\(=\left(y+z+x\right)\cdot\left(xy+xz+yz\right)\)
c: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2+2xyz\right)+\left(y^2z+yz^2\right)\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2+2xz\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)
\(=\left(y+z\right)\left(x^2+yz+xy+xz\right)\)
\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)
xy(x - y) - 7(x - y) = (x - y)(xy - 7)