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Bài 1:
a)\(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
b)\(x^3-2xy-x^2y+2y^2=\left(x^3-x^2y\right)-\left(2xy-2y^2\right)=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
c)Đề sai hoàn toàn
d) \(2x^2+4xy+2y^2-8z^2=2\left(x^2+2xy+y^2-4z^2\right)=2\left[\left(x+y\right)^2-\left(2z\right)^2\right]=2\left(x+y-2z\right)\left(x+y+2z\right)\)e) \(3x-3a+yx-ya=3\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(3+y\right)\)
f)\(\left(x^2+y^2\right)^2-4x^2y^2=\left(x-y\right)^2\left(x+y\right)^2\)
g)\(2x^2-5x+2=2x^2-x-4x+2=x\left(2x-1\right)-2\left(2x-1\right)=\left(2x-1\right)\left(x-2\right)\)
i)\(14x\left(x-y\right)-21y\left(y-x\right)+28z\left(x-y\right)=14x\left(x-y\right)+21y\left(x-y\right)+28z\left(x-y\right)=7\left(x-y\right)\left(2x+3y+4z\right)\)
a: Sửa đề: x^3-x^2+5x-5
=x^2(x-1)+5(x-1)
=(x-1)(x^2+5)
b: x^3+4x^2+x-6
=x^3-x^2+5x^2-5x+6x-6
=(x-1)(x^2+5x+6)
=(x-1)(x+2)(x+3)
c: \(=\left(x+2\right)^3+y^3\)
\(=\left(x+2+y\right)\left(x^2+4x+4-xy-2y+y^2\right)\)
a ) \(\left(x+y+z\right)^2=x^2+y^2+z^{2^{ }}+2xy+2yz+2zx\)
Biến đổi vế trái ta được :
\(\left(x+y+z\right)^2=\left(x+y+z\right)\left(x+y+z\right)\)
\(=x^2+xy+xz+xy+y^2+yz+zx+zy+z^2\)
\(=x^2+y^2+z^{2^{ }}+2xy+2yz+2zx\)
Vậy \(\left(x+y+z\right)^2=x^2+y^2+z^{2^{ }}+2xy+2yz+2zx\)
x3-x+3x2y+3xy2+y3-y
=x2(x-1)+3(x2y+xy2)+y2(y-1)
=x2(x-1)+3(x2.y+y2.x)+y2(y-1)
=x2(x-1)+3{[x(x+1)+y(y+1)]}+y2(y-1)
=x2(x-1)+3.x(x+1)+3.y(y+1)+y2(y-1)
=x2(x-1)+2x2+3.x(x+1)+3.y(y+1)+y2(y-1)+2y2-2x2-2y2
=x2(x+1)+3.x(x+1)+3.y(y+1)+y2(y+1)-2x2-2y2
=(x2+3)(x+1)+(y2+3)(y+1)-2(x2+y2)
a, ( x + y )3 - x3 - y3 = x3+3x2y+3xy2+y3- x3 - y3 = 3x2y+3xy2 = 3xy( x + y)
b, x3 + y3 + z3 - 3xyz = x3 + 3x2y+3xy2+y3 + z3 - 3x2y-3xy2 -3xyz = (x+y)^3 + z^3 - 3xy( x + y + z)
(x+y+z)[(x+y)^2 - (x+y)z + z^2 ] - 3xy( x + y + z) = (x+y+z) ( x^2 + 2xy + y^2 - xz - yz + z^2 ) - 3xy(x+y+z)
= (x+y+z) ( x^2 + 2xy + y^2 - xz - yz + z^2 - 3xy)
bài tieps theo thì tách từng cái ra rồi rút gọc, còn bnhiu thì đưa 3 ra ngoài
c,= (x2+ y2)3 + [(y2 + z2) - (x2 + y2)]3 - (y2 + z2)3
= (x2 + y2)3 + (y2 + z2)3 - 3(y2 + z2)2(x2 + y2) + 3(y2 + z2)(x2 + y2)2 - (x2+ y2)3 + (x2+ y2)3
= 3(y2 + z2)(x2 + y2)(x2 - z2)
= 3(x + z)(x - z)(y2 + z2)(x2 + y2)
Cách làm:
b ) (x+y+z)3=x3+y3+z3+3(x+y)(y+z)(z+x)
Biến đổi vế trái ta được :
(x+y+z)3=(x+y+z)(x+y+z)(x+y+z)
=x3+y3+z3+3x2y+3x2z+3xy2+3y2z+3xz2+3yz2+6xyz
=x3+y3+z3+3(x+y)(y+z)(z+z
Vậy (x+y+z)3=x3 3+z3+3(x+y)(y+z)(z+x)