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a, \(14x^2y-21xy^2-28x^2y^2=7xy\left(2x-3y-4xy\right)\)
b,\(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
c,\(10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x-8\right)\)
d,\(\left(3x+1\right)^2-\left(x+1\right)^2=9x^2+6x+1-x^2-2x-1=7x^2-4x=x\left(7x-4\right)\)
e,\(x^3+y^3+z^3-3xyz=\)
x
5x^2 - 10xy + 5y^2 - 20z^2
=5[(x-y)^2 - (2z)^2]=5(x-y-2z)(x-y+2z)
vào bệnh viện hoặc đến nơi khám chữa bệnh gần nhà nhất ko kịp thì die
a)
\(14x^2y-21xy^2+28x^2y^2\)
\(=7xy(2x-3y+4xy)\)
b) \(x(x+y)-5x-5y=x(x+y)-5(x+y)=(x-5)(x+y)\)
c)
\(10x(x-y)-8(y-x)=10x(x-y)+8(x-y)\)
\(=(x-y)(10x+8)=2(x-y)(5x+4)\)
a. \(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(2x-3y+4xy\right)\)
b. \(x\left(x+y\right)-5x-5y\)
\(=x\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x-5\right)\left(x+y\right)\)
c. \(10x\left(x-y\right)-8\left(y-x\right)\)
\(=10x\left(x-y\right)+8\left(x-y\right)\)
\(=\left(10x+8\right)\left(x-y\right)\)
d. \(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)
\(=2x\left(4x+2\right)\)
\(=4x\left(2x+1\right)\)
e. Vì bài này giải không ra nên mình nghĩ nó sai đề, sửa lại tí nhé!
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz+zy+z^2-3xy\right)\)
g. \(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2-4z^2\right)\)
\(=5\left[\left(x-y^2\right)-4z^2\right]\)
\(=5\left(x-y+z\right)\left(x-y-z\right)\)
h. \(x^3-x+3x^2y+3xy^3+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
i. \(x^2+7x-8\)
\(=x^2-x+8x-8\)
\(=x\left(x-1\right)+8\left(x-1\right)\)
\(=\left(x+8\right)\left(x-1\right)\)
a) \(x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
a) \(^{x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)}\)
b)\(a^3-a^2x-ay=a\left(a^2-a.x-y\right)\)
c)\(5x^2-10xy+5y-20z^2=-20z^2+\left(5-10x\right)y+5x^2 \)
\(=-5\left(4z^2+2xy-y-x^2\right)\)
d)\(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3xy^2+3x^2y+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
h) \(=3x\left(2y-3z\right)\left[x^2-5\left(2y-3z\right)\right]=3x\left(2y-3z\right)\left(x^2-10y+15z\right)\)
k) \(=\left(x+2\right)\left(3x-5\right)\)
l) \(=\left(18^2+3\right)\left(x+3\right)=327\left(x+3\right)\)
m) \(=7xy\left(2x-3y+4xy\right)\)
n) \(=2\left(x-y\right)\left(5x-4y\right)\)
\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)
\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)