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LC
3
7 tháng 8 2015
a) 10x(x-y) - 8y(y-x)
= 10x(x-y) + 8y(x-y)
= (10x-8y)(x-y)
b) x^2 - 2xy + y^2 - 25
=( x- y)^2 - 25
= ( x- y- 5 )( x- y+ 5 )
c) 5x^2 + 10x^2y + 5xy^2
= 5( x^2 + 2x^2y + xy^2)
= 5x ( x + 2xy + y^2)
( 5x^3 hay 5x^2)
NP
4
21 tháng 8 2017
\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(x-y\right)\left(5x+4y\right)\)
5 tháng 9 2017
a) \(5x^2\)\(\left(x-2y\right)\)\(-\)\(15x\)\(\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
b) \(3\left(x-y\right)\)\(-\)\(5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
c) \(10x\left(x-y\right)\)\(-\)\(8y\left(y-x\right)\)
\(=\)\(10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(5x+4\right)\left(x-y\right)\)
d) \(x^2\)\(\left(x-5\right)\)\(+\)\(4\)\(\left(5-x\right)\)
\(=x^2\)\(\left(x-5\right)\)\(-\)\(4\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-4\right)\)
\(=\left(x-5\right)\left(x-2\right)\left(x-2\right)\)
5 tháng 9 2017
a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=\left(x-2y\right)\left(x-3\right)5x\)
b)\(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(3+5x\right)\left(x-y\right)\)
c)\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(10x+8y\right)\left(x-y\right)\)
\(=2\left(5x+4y\right)\left(x-y\right)\)
d)\(x^2\left(x-5\right)+4\left(5-x\right)\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x^2-4\right)\left(x-5\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
3 tháng 10 2017
\(x^2-y^2+10x+8y+9\)
\(=x^2-y^2+9x+x+9y-y+9\)
\(=\left(x^2-y^2\right)+\left(x-y\right)+\left(9x+9y+9\right)\)
\(=\left(x-y\right)\left(x+y\right)+\left(x-y\right)+9\left(x+y+1\right)\)
\(=\left(x-y\right)\left(x+y+1\right)+9\left(x+y+1\right)\)
\(=\left(x+y+1\right)\left(x-y+9\right)\)
LH
1
7 tháng 11 2021
\(A=\dfrac{7yz}{x}+\dfrac{8zx}{y}+\dfrac{9xy}{z}=\dfrac{3yz}{x}+\dfrac{3zx}{y}+\dfrac{4yz}{x}+\dfrac{4xy}{z}+\dfrac{5zx}{y}+\dfrac{5xy}{z}\)
\(bddt:\) \(AM-GM\Rightarrow\left\{{}\begin{matrix}\dfrac{3yz}{x}+\dfrac{3zx}{y}\ge2\sqrt{\dfrac{9yzxz}{xy}}\ge6z\\\dfrac{4yz}{x}+\dfrac{4xy}{z}\ge2\sqrt{\dfrac{16yzxy}{xz}}\ge8y\\\dfrac{5zx}{y}+\dfrac{5xy}{z}\ge2\sqrt{\dfrac{25zxxy}{yz}}\ge10x\\\end{matrix}\right.\)
\(\Rightarrow A\ge10x+8y+6z\)
VM
3
3 tháng 10 2021
a) \(x^2-3x=x\left(x-3\right)\)
b) \(10x\left(x-y\right)-8y\left(x-y\right)=2\left(x-y\right)\left(5x-4y\right)\)
c) \(x^2-9=\left(x-3\right)\left(x+3\right)\)
11 tháng 10 2020
a) x2 + 4y + 4y2 + 26 - 10x = ( x2 - 10x + 25 ) + ( 4y2 + 4y + 1 ) = ( x - 5 )2 + ( 2y + 1 )2
b) 4y2 + 34 - 10x + 12y + x2 = ( x2 - 10x + 25 ) + ( 4y2 + 12y + 9 ) = ( x - 5 )2 + ( 2y + 3 )2
c) -10x + y2 - 8y + x2 + 41 = ( x2 - 10x + 25 ) + ( y2 - 8y + 16 ) = ( x - 5 )2 + ( y - 4 )2
d) x2 + 9y2 - 12y + 29 - 10x = ( x2 - 10x + 25 ) + ( 9y2 - 12y + 4 ) = ( x - 5 )2 + ( 3y - 2 )2
11 tháng 10 2020
a) \(x^2+4y+4y^2+26-10x\)
\(=\left(x^2-10x+25\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-5\right)^2+\left(2y+1\right)^2\)
b) \(4y^2+34-10x+12y+x^2\) đề ntn à?
\(=\left(4y^2+12y+9\right)+\left(x^2-10x+25\right)\)
\(=\left(2y-3\right)^2+\left(x-5\right)^2\)
c) \(-10x+y^2-8y+x^2+41\)
\(=\left(x^2-10x+25\right)+\left(y^2-8y+16\right)\)
\(=\left(x-5\right)^2+\left(y-4\right)^2\)
d) \(x^2+9y^2-12y+29-10x\)
\(=\left(x^2-10x+25\right)+\left(9y^2-12y+4\right)\)
\(=\left(x-5\right)^2+\left(3y-2\right)^2\)
KQ
0
`10x(x-y) - 8y(y-x)`
`= 10x(x-y) + 8y(x-y)`
`= (10x+8y)(x-y)`
`= 2(5x+4y)(x-y)`
\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\cdot\left(x-y\right)-8y\cdot-\left(x-y\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(10x+8y\right)\left(x-y\right)\)
\(=\left(2\cdot5x+2\cdot4y\right)\left(x-y\right)\)
\(=2\left(5x+4y\right)\left(x-y\right)\)