Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3x^2-3y^2-2\left(x^2-2xy+y^2\right)\)
\(=3x^2-3y^2-2x^2+4xy-2y^2\)
\(=x^2+4xy-5y^2\)
\(=x^2+4xy+4y^2-9y^2\)
\(=\left(x+2y\right)^2-\left(3y\right)^2\)
\(=\left(x+2y-3y\right)\left(x+2y+3y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
A/ \(16x-5x^2-3=\left(15x-3\right)-\left(5x^2-x\right)=3\left(5x-1\right)-x\left(5x-1\right)=\left(5x-1\right)\left(3-x\right)\)
B/ \(x^3-3x^2+1-3x=\left(x^3-4x^2+x\right)+\left(x^2-4x+1\right)=x\left(x^2-4x+1\right)+\left(x^2-4x+1\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
C/ \(x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
D/ \(\left(2x+1\right)^2-\left(x-1\right)^2=\left(2x+1-x+1\right)\left(2x+1+x-1\right)=3x\left(x+2\right)\)
x3+y(1-3x2)+x(3y2-1)-y3
= x3-3x2y+3xy2-y3+y-x
=(x-y)3 -(x-y)
=(x-y)(x2-2xy+y2-1)
cái chỗ kia giải thích dùm mìh đy : \(x^3-3x^2y+3xy^2-y^3+y-x\)
\(x^3+y\left(1-3x^2\right)+x\left(3y^2-1\right)-y^3\)
\(=x^3-3x^2y+3xy^2-y^3+y-x\)
\(=\left(x-y\right)^3-\left(x-y\right)\)
phân tích đa thức thành nhân tử cơ mà
=(x-y)3-(x-y)
=(x-y)[(x-y)2-1]
a) \(A=x^2-2xy+y^2+3x-3y-4\)
\(=\left(x-y\right)^2-1+3x-3y-3\)
\(=\left(x-y-1\right)\left(x-y+1\right)+3\left(x-y-1\right)\)
\(=\left(x-y-1\right)\left(x-y+1+3\right)\)
\(=\left(x-y-1\right)\left(x-y+4\right)\)
\(\left(2x-y\right)\left(x-y\right)-\left(3y-4x\right)^2+\left(y-2x\right)\left(2y-3x\right)\)
=(2x-y)(x-y)-(2x-y)(2y-3x)-(4x-3y)2
=(2x-3y)(x-y-2y+3x)-(4x-3y)2
=(2x-3y)(4x-3y)-(4x-3y)2
=(4x-3y)(2x-3y-4x+3y)
=(4x-3y))(-2x)
x2 + y2 - 3x - 3y + 2xy
= ( x2 + 2xy + y2 ) - ( 3x + 3y )
= ( x + y )2 - 3( x + y )
= ( x + y )( x + y - 3 )
b) ( x2 - 4x )2 - 2( x - 2 )2 - 7
= ( x2 - 4x )2 - 2( x2 - 4x + 4 ) - 7 (*)
Đặt t = x2 - 4x
(*) <=> t2 - 2( t + 4 ) - 7
= t2 - 2t - 8 - 7
= t2 - 2t - 15
= t2 + 3t - 5t - 15
= t( t + 3 ) - 5( t + 3 )
= ( t + 3 )( t - 5 )
= ( x2 - 4x + 3 )( x2 - 4x - 5 )
= ( x2 - x - 3x + 3 )( x2 + x - 5x - 5 )
= [ x( x - 1 ) - 3( x - 1 ) ][ x( x + 1 ) - 5( x + 1 ) ]
= ( x - 1 )( x - 3 )( x + 1 )( x - 5 )
a) Ta có: \(x^2+y^2-3x-3y+2xy\)
\(=\left[\left(x^2+y^2+2xy\right)-2\left(x+y\right)+1\right]-\left(x+y+1\right)\)
\(=\left[\left(x+y\right)^2-2\left(x+y\right)+1\right]-\left(x+y+1\right)\)
\(=\left(x+y-1\right)^2-\left(x+y+1\right)\)
\(=\left(x+y-1\right)^2-\left(\sqrt{x+y+1}\right)^2\)
\(=\left(x+y-1+\sqrt{x+y+1}\right)\left(x+y-1-\sqrt{x+y+1}\right)\)
a) = (x + 1)^3 - 27z^3 = (x+1 - 3z)( (x+1)^2 + 3z(x+1) + 9z^2 )
b)= x^2 + x+ 3x + 3 = x (x+1) +3 (x+1) =(x+3)(x+1)
c) = 2x^2 - 2x + 5x - 5 = 2x(x-1) + 5(x-1) = (2x+5)(x-1)
d) = (a^2 + 1 - 2a)(a^2 +2a +1) = (a-1)^2 * (a+1)^2
e) = x^3 ( x-1) - (x^2 - 1) = x^3 ( x-1) - (x+1)(x-1) = (x^3 -x -1)(x-1)
Ta có: \(3x^2\left(y-x\right)+6x^2\left(x-y\right)^2\)
\(=3x^2\left(y-x\right)+6x^2\left(y-x\right)^2\)
\(=3x^2\left(y-x\right)\left[1-2\left(y-x\right)\right]\)
\(=3x^2\left(y-x\right)\left(2x-2y+1\right)\)
3x2( y - x ) + 6x2( x - y )2
= 3x2( y - x ) + 6x2( y - x )2
= 3x2( y - x )[ 1 + 2( y - x ) ]
= 3x2( y - x )( 2y - 2x + 1 )
\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3x^2-3y^2-2\left(x^2-2xy+y^2\right)\)
\(=3x^2-3y^2-2x^2+4xy-2y^2\)
\(=x^2+4xy-5y^2\)
\(=x^2+4xy+4y^2-9y^2\)
\(=\left(x+2y\right)^2-\left(3y\right)^2\)
\(=\left(x+2y-3y\right)\left(x+2y+3y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)