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30 tháng 9 2017

1)

a \(x^3+y^3+x^2z+y^2z-xyz\)

=(x+y)(x2-xy+y2)+z(x2-xy+y2)

=(x+y+z)(x^2-xy+y^2)

b)yz(y+z)+xz(z-x)-xy(x+y)

=yz2+y2z+xz2-x2z-x2y-xy2

=z2(x+y)-z(x2-y2)-xy(x+y)

=(z2-xy)(x+y)-z(x-y)(x+y)

=(z2-xy-zx+zy)(x+y)

=[z(z-x)+y(z-x)](x+y)

=(z+y)(z-x)(x+y)

30 tháng 9 2017

==1)

a) x3+y3+x2z+y2z-xyz

= ( x+y)(x2-xy+y2)+z(x2+y2-xy)

=(x2+y2-xy)(x+y+z)

b) yz(y+z)+xz(z-x)-xy(x+y)

=y2z+yz2+xz(z-x)-x2y-xy2

=(y2z-xy2)+(yz2-xy2)+xz(z-x)

=y2(z-x)+y(z2-x2)+xz(z-x)

=(z-x)(y2+xz)+y(z+x)(z-x)

=(z-x)(y2+xz+yz+xy)

=(z-x)(y(y+z)+x(z+y))

=(z-x)(y+z)(x+y)

8 tháng 3 2022

a) \(B=x^3+x^2z+y^2z-xyz+y^3\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)+z\left(x^2-xy+y^2\right)\)

\(=\left(x^2-xy+y^2\right)\left(x+y+z\right)\)

b) \(B=\left(x^2-xy+y^2\right)\left(x+y+z\right)=x^2-xy+y^2\)

\(=x^2-2.x.\dfrac{1}{2}y+\dfrac{1}{4}y^2+\dfrac{3}{4}y^2=\left(x-\dfrac{1}{2}y\right)^2+\dfrac{3}{4}y^2\ge0\)

Dấu bằng xảy ra khi \(x=y=0\)

22 tháng 10 2021

\(a,=\left(xy-1-x-y\right)\left(xy-1+x+y\right)\\ b,Sửa:a^3+2a^2+2a+1\\ =a^3+a^2+a^2+a+a+1=\left(a+1\right)\left(a^2+a+1\right)\\ c,=1-4a^2-a\left(a^2-4\right)=1-4a^2-a^3+4a\\ =\left(1-a\right)\left(1+a+a^2\right)+4a\left(1-a\right)\\ =\left(1-a\right)\left(1+5a+a^2\right)\\ d,=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\\ =a^2\left(1-b\right)\left(1+b\right)+b\left(b-1\right)+a\left(b-1\right)\\ =\left(b-1\right)\left(-a^2-ab+b+a\right)\\ =\left(b-1\right)\left(b-1\right)\left(a+b\right)\left(1-a\right)\)

\(e,=x^2y+xy^2-yz\left(y+z\right)+x^2z-xz^2\\ =\left(x^2y+x^2z\right)+\left(xy^2-xz^2\right)-yz\left(y+z\right)\\ =x^2\left(y+z\right)+x\left(y-z\right)\left(y+z\right)-yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy-xz-yz\right)\\ =\left(y+z\right)\left(x+y\right)\left(x-z\right)\)

\(f,=xyz-xy-yz-xz+x+y+z-1\\ =xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(x-1\right)\\ =\left(z-1\right)\left(xy-y-x+1\right)=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)

21 tháng 3 2017

25 tháng 6 2017

27 tháng 10 2023

b: \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

\(=x^2y+xy^2-y^2z-yz^2+x^2z-xz^2\)

\(=x^2y-yz^2+xy^2-y^2z+x^2z-xz^2\)

\(=y\left(x-z\right)\left(x+z\right)+y^2\left(x-z\right)+xz\left(x-z\right)\)

\(=\left(x-z\right)\left(xy+yz+y^2+xz\right)\)

\(=\left(x-z\right)\left(x+y\right)\left(x+z\right)\)

 

17 tháng 11 2019

a) (x - 1)(x + l)(x - 2)(x - 4).      b) (x - 2)( x 2  + 4).

c) 2y(3 x 2   +   y 2 ).                          d) 2(x + y + z) ( a   -   b ) 2 .

24 tháng 8 2021

a. \(x^2\left(x-3\right)^2-\left(x-3\right)^2-x^2+1\)

\(=\left(x-3\right)^2\left(x^2-1\right)-\left(x^2-1\right)\)

\(=\left[\left(x-3\right)^2-1\right]\left(x^2-1\right)\)

\(=\left(x-3+1\right)\left(x-3-1\right)\left(x+1\right)\left(x-1\right)\)

\(=\left(x-2\right)\left(x-4\right)\left(x+1\right)\left(x-1\right)\)

b. \(x^3-2x^2+4x-8\)

\(=\left(x^3+4x\right)-\left(2x^2+8\right)\)

\(=x\left(x^2+4\right)-2\left(x^2+4\right)\)

\(=\left(x-2\right)\left(x^2+4\right)\)

c. \(\left(x+y\right)^3-\left(x-y\right)^3\)

\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)\)

\(=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3\)

\(=6x^2y+2y^3\)

\(=2y\left(3x^2+y^2\right)\)

d. \(2a^2\left(x+y+z\right)-4ab\left(x+y+z\right)+2b^2\left(x+y+z\right)\)

\(=\left(2a^2-4ab+2b^2\right)\left(x+y+z\right)\)

\(=2\left(a^2-2ab+b^2\right)\left(x+y+z\right)\)

\(=2\left(a-b\right)^2\left(x+y+z\right)\)