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a) a2−b2−4a+4
=(a2-4a+4)-b2
=(a-2)2-b2
=(a-2-b)(a-2+b)a2−b2−4a+4
b) x2+2x−3
=x2-x+3x-3
=x(x-1)+3(x-1)
=(x+3)(x-1)x2+2x−3
c) 4x2y2−(x2+y2)2
=(2xy-x2-y2)(2xy+x2+y2)
=-(x-y)2(x+y)2
d) 2a3−54b3
=2(a3-27b3)
=2(a-3b)(a2+3ab+9b2)
a) 5x2 - 5xy + 7y - 7x = ( 5x2 - 5xy ) - ( 7x - 7y ) = 5x( x - y ) - 7( x - y ) = ( x - y )( 5x - 7 )
b) x2 - y2 + 2x + 1 = ( x2 + 2x + 1 ) - y2 = ( x + 1 )2 - y2 = ( x - y + 1 )( x + y + 1 )
c) 3x2 + 6xy + 3y2 - 3z2 = 3( x2 + 2xy + y2 - z2 ) = 3[ ( x2 + 2xy + y2 ) - z2 ] = 3[ ( x + y )2 - z2 ] = 3( x + y - z )( x + y + z )
d) ab( x2 + y2 ) + xy( a2 + b2 ) = abx2 + aby2 + a2xy + b2xy
= ( a2xy + abx2 ) + ( aby2 + b2xy )
= ax( ay + bx ) + by( ay + bx )
= ( ay + bx )( ax + by )
a) x2 + 4x + 3 - y2 -2y
= x2 +4x + 4 - y2 -2y-1
= (x+2)2 - (y+1)2
= (x+2-y-1).(x+2+y+1)
= (x-y+1).(x+y+3)
b) 2a2 -5ab + 2b2
= 2a2 -4ab + 2b2 - ab
= 2.(a2 - 2ab+b2) - ab
= 2.(a-b)2 -ab
...
c) (x+y)2 - 2x - 2y + 1
= (x+y)2 - 1 - 2x -2y +2
= (x+y-1).(x+y+1) - 2.(x+y-1)
= (x+y-1)2
- =>((x-5)(x+5))2-(x-5)2 => (x-5)2(x+5)2-(x-5)2 => (x-5)2 ((x+5)2-1) => (x2+10x+25)(x+6)(x+4)
a)\(ax-2x-a^2+2a\)
\(=\left(ax-2x\right)-\left(a^2-2a\right)\)
\(=x\left(a-2\right)-a\left(a-2\right)\)
\(=\left(x-a\right)\left(a-2\right)\)
b)\(x^2+x-ax-a\)
\(=\left(x^2+x\right)-\left(ax+a\right)\)
\(=x\left(x+1\right)-a\left(x+1\right)\)
\(=\left(x-a\right)\left(x+1\right)\)
c)\(2x^2+4ax+x+2a\)
\(=\left(2x^2+4ax\right)+\left(x+2a\right)\)
\(=2x\left(x+2a\right)+\left(x+2a\right)\)
\(=\left(2x+1\right)\left(x+2a\right)\)
d)\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3\left(x+y\right)-2\left(x-y\right)\right)\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
Phân tích đa thức sau thành nhân tử:
a/ ax - 2x - a2 +2a
= x(a-2)-a(a-2)
= (a-2)(x-a)
b/x2 + x - ax - a
= x(x+1)-a(x+1)
=(x+1)(x-a)
c/2x2 + 4ax +x +2a
= x(2x+1)+2a(2x+1)
= (2x+1)(x+2a)