bài 2 phân tích các đa thức sau thành nhân tử
a,(x-z)^2-y^2+2y-1 b,1-2a+2bc+a^2-b^2-c^2
c,x^2+y^@-2xy-x+y d,x^2+3cd(2-3cd)-10xy-1+25y^2
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V
3 tháng 10 2015
1)
b) \(\left(x-z\right)^2-y^2+2y-1\)
\(=\left(x^2-2xz+z^2\right)-\left(y-1\right)^2\)
\(=\left(y-z\right)^2-\left(y-1\right)^2\)
\(=\left[\left(x-z\right)+\left(y-1\right)\right]\cdot\left[\left(x-z\right)-\left(y+1\right)\right]\)
\(=\left(x-z+y-1\right)\cdot\left(x-z-y-1\right)\)
DH
27 tháng 7 2017
a, \(\left(x-z\right)^2-y^2+2y-1\)
\(=\left(x-z\right)^2-\left(y-1\right)^2\)
\(=\left(x-z-y+1\right)\left(x-z+y-1\right)\)
b, \(x^3+y^3+3y^2+3y+1\)
\(=x^3+\left(y+1\right)^3=\left(x+y+1\right)\left[x^2-x\left(y+1\right)+\left(y+1\right)^2\right]\)
\(=\left(x+y+1\right)\left(x^2-xy-x+y^2+2y+1\right)\)
c, \(1-2a+2bc+a^2-b^2-c^2\)
\(=a^2-2a+1-\left(b^2-2bc+c^2\right)\)
\(=\left(a-1\right)^2-\left(b-c\right)^2\)
\(=\left(a-1-b+c\right)\left(a-1+b-c\right)\)
d, \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)
\(=\left(x^2-10xy+25y^2\right)+\left[3cd\left(2-3cd\right)-1\right]\)
\(=\left(x-5y\right)^2+\left(6cd-\left(3cd\right)^2-1\right)\)
\(=\left(x-5y\right)^2-\left(3cd-1\right)^2\)
\(=\left(x-5y-3cd+1\right)\left(x-5y+3cd-1\right)\)
Chúc bạn học tốt!!!
A
27 tháng 7 2017
Giúp bạn câu e nè
e) bc ( b + c) + ac ( c - a) - ab ( a + b)
= b2 c + bc2 + ac 2 - a2c - a2b - ab2
= ( b2 c - a2c ) + ( bc2+ ac2 ) - ( a2b + ab2 )
= c ( b2- a2 ) + c2 ( b+ a ) - ab(a + b)
= c( b - a )( b + a) + c2 ( b+ a ) - ab(a + b)
= ( b+ a )( bc - ac + c2- ab )
= ( b+ a )( ( bc - ab ) - ( ac - c2 ))
= ( b+ a )( b( c - a ) - c ( a - c))
= ( b+ a )( b( c - a ) + c ( c - a))
= ( b+ a )( c - a )(b + c )
12 tháng 10 2021
Bài 2:
a: \(3x^2-3xy=3x\left(x-y\right)\)
b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)
d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)
L
1 tháng 8 2021
a) \(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(2-x+y\right)\)
1 tháng 8 2021
b) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+y^3\right)+\left(3x^2+3xy^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+3xy-1\right)\)
\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)
22 tháng 9 2016
1
a, 2x2+4x+2-2y2 = 2(x2+2x+1-y2)= 2[(x+1)2-y2 ] = 2(x-y+1)(x+y+1)
b, 2x - 2y - x2 + 2xy - y2= 2(x -y) - (x2 - 2xy + y2) = 2(x-y)-(x-y)2=(x-y)(2-x+y)
c, x2-y2-2y-1=x2-(y2+2y+1)=x2-(y+1)2=(x-y-1)(x+y+1)
d, x2-4x-2xy-4y+y2= x2-2xy+y2-4x-4y=(x-y)
2.
a, x2-3x+2=x2-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)
b, x2+5x+6=x2+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)
c, x2+6x-6=
a)(x-z)^2-y^2+2y-1=(x-z)^2-(y^2-2y+1) b)1-2a+2bc+a^2-b^2-c^2=a^2-2a+1-b^2+2bc-c^2
=(x-z)^2-(y-1)^2 =(a-1)^2-(b^2-2bc+c^2)
=(x-z-y+1)(x-z+y-1) =(a-1)^2-(b-c)^2
=(a-1-b+c)(a-1+b-c)
c)x^2+y^2-2xy-x+y=x^2-2xy+y^2-(x-y)
=(x-y)^2-(x-y)
=(x-y)(x-y-1)
câu (d) có sai đề ko vậy@@