Phân tích đa thức thành nhân tử :
x^2+4y^2+9-4xy-6x+12y
Giúp mìk vs đc hok!
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^2+4xy+4y^2-4z^2-1-4z\)
\(=x^2+4xy+4y^2-\left(4z^2+4z+1\right)\)
\(=\left(x+2y\right)^2-\left(2z+1\right)^2\)
\(=\left(x+2y+2z+1\right)\left(x+2y-2z-1\right)\)
= ( x2 + 4xy +4y2 ) - ( 4z2 +4z +1 )
= ( x + y )2 - [ (2z)2 - 2z.1 +12)]
= ( x + y )2 - (2z+1)2
= ( x + y - 2z - 1 ).( x + y + 2z + 1 )
=\(x^2+2.x.2y+\left(2y\right)^2-\left[\left(2z\right)^2+2.2z.1+1^2\right]=\left(x+2y\right)^2-\left(2z+1\right)^2=\left(x+2y+2z+1\right)\left(x+2y-2z-1\right)\)
\(-\left(x+2y\right)^2\)
\(-\left(x-3\right)^2\)
\(\left(3-5x\right)^2\)
\(-x^2-4xy-4y^2=-\left(x+2y\right)^2\)
\(-x^2+6x-9=-\left(x-3\right)^2\)
\(25x^2-30x+9=\left(5x-3\right)^2\)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
3 - 6x + 3x^2
= 3 ( 1 - 2x + x^2 )
= 3( 1 - x )^2
b, x^2 - 4xy + 4y^2
= ( x)^2 + 2.x.2y + (2y)^2
= ( x+ 2y)^2
\(=\left(x^2-6x+9\right)-4y^2\)
\(=\left(x-3\right)^2-\left(2y\right)^2\)
\(=\left(x-3-2y\right)\left(x-3+2y\right)\)
= ( x^2 - 4y^2 ) + ( 9 - 6x)
= [ x^2 - (2y)^2 ] + 3( 3 - 2x )
= (x - 2y)(x + 2y)+ 3(3 - 2x)
\(x^2+4y^2+9-4xy-6x+12y\)
\(=\left(x^2-4xy+4y^2\right)+\left(-6x+12y\right)+9\)
\(=\left(x-2y\right)^2-6\left(x-2y\right)+9\)
\(=\left(x-2y-3\right)^2\)