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MP
2
KN
8 tháng 8 2019
\(\left(x-3y\right)\left(x^2+3xy+9y^2\right)+\left(x+3y\right)\left(x^2-3xy+9y^2\right)\)
\(=x^3-27y^3+x^3+27y^3=2x^3=2.\left(-1\right)^3=-2\)
NK
1
KT
10 tháng 8 2018
đk: \(x\ne0\); \(x\ne\pm3y\)
\(\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}\)
\(=\frac{x+9y}{\left(x-3y\right)\left(x+3y\right)}-\frac{3y}{x\left(x+3y\right)}\)
\(=\frac{x\left(x+9y\right)}{x\left(x-3y\right)\left(x+3y\right)}-\frac{3y\left(x-3y\right)}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\frac{x^2+9xy-3xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\frac{\left(x+3y\right)^2}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\frac{x+3y}{x\left(x-3y\right)}\)
NL
1
27 tháng 11 2018
\(\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}=\frac{x+9y}{\left(x-3y\right)\left(x+3y\right)}-\frac{3y}{x\left(x+3y\right)}\)
\(=\frac{x\left(x+9y\right)-3y\left(x-3y\right)}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\frac{x^2+9xy-3xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\frac{x^2+6xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}=\frac{\left(x+3y\right)^2}{x\left(x-3y\right)\left(x+3y\right)}=\frac{x+3y}{x\left(x-3y\right)}\)
CN
24 tháng 12 2017
\(\dfrac{x+9y}{x^2-9y^2}-\dfrac{3y}{x^2+3xy}\)
\(=\dfrac{x+9y}{\left(x-3y\right)\left(x+3y\right)}-\dfrac{3y}{x\left(x+3y\right)}\)
\(=\dfrac{x\left(x+9y\right)-3y\left(x-3y\right)}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\dfrac{x^2-6xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\dfrac{\left(x-3y\right)^2}{x\left(x-3y\right)\left(x+3y\right)}\)
\(=\dfrac{x-3y}{x\left(x+3y\right)}\)
CC
1
AM
29 tháng 6 2015
\(\left(x+3y\right)^3-\left(x+3y\right)\left(x^2-3xy+9y^2\right)-2x\left(x-2\right)^2=\left(x+3y\right)^3-\left(x^3+27y^3\right)-2x\left(x-2\right)^2\)
Thay x=1 y=2 ta có:
\(\left(1+3.2\right)^3-\left(1^3+27.2^3\right)-2.1.\left(1-2\right)^2=7^3-\left(1+216\right)-2=343-217-2=124\)
12 tháng 7 2017
1) (x+3)(x2- 3x + 9) = x3 + 27
2) (x2 + 2y)2 = x4 + 4xy + 4y2
3) (2x-3)(2x+3) = 4x2 - 9
4) (x + 3y)3 = x3 + 9x2y + 9xy2 + y3
5) (2x2- y)3 = 8x6 - 6x4y + 6x2y2 - y3
6) (x-3y)(x2 + 3xy +9y2)= x3- 27y3
7) (2x + 3y)(4x2 - 6xy +9y2)= 8x3 + 27y3
8) (3x - y2)2= 9x2 - 6xy2 + y4
1)2xy−2y²+3x−3y1)2xy−2y²+3x−3y
=2y(x−y)+3(x−y)=2y(x−y)+3(x−y)
=(2y+3)(x−y)=(2y+3)(x−y)
2)x²−9y²+x+3y2)x²−9y²+x+3y
=x²−(3y)²+(x+3y)=x²−(3y)²+(x+3y)
=(x−3y)(x+3y)+(x+3y)=(x−3y)(x+3y)+(x+3y)
=(x−3y+1)(x+3y)=(x−3y+1)(x+3y)
3)3x(2x−3)−6x+93)3x(2x−3)−6x+9
=3x(2x−3)−3(2x−3)=3x(2x−3)−3(2x−3)
=(3x−3)(2x−3)=(3x−3)(2x−3)
=3(x−1)(2x−3)=3(x−1)(2x−3)
4)y²−25−x²−10x4)y²−25−x²−10x
=−(x²+10x+25)+y²=−(x²+10x+25)+y²
=−(x+5)²+y²=−(x+5)²+y²
=y²−(x+5)²=y²−(x+5)²
=(y−x−5)(y+x+5)=(y−x−5)(y+x+5)
5)x²−10x+245)x²−10x+24
=x²−4x−6x+24=x²−4x−6x+24
=x(x−4)−6(x−4)=x(x−4)−6(x−4)
=(x−6)(x−4)