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\(\left(a^2+b^2+ab\right)^2-a^2b^2-b^2c^2-c^2a^2=\left(a^2+b^2+ab-ab\right)\left(a^2+b^2+2ab\right)-c^2\left(a^2+b^2\right)\)
\(=\left(a^2+b^2\right)\left(a+b\right)^2-c^2\left(a^2+b^2\right)=\left(a^2+b^2\right)\left(a+b-c\right)\left(a+b+c\right)\)
1/ 2a + 2b = 2( a + b )
2/ 3a - 6b - 9c = 3( a - 2b - 3c )
3/ 5ax - 15ay + 20a = 5a( x - 3y + 4 )
4/ 3a2x - 6a2y + 12a = 3a( ax - 2ay + 4 )
5/ 4a( x - 5 ) - 2( 5 - x ) = 4a( x - 5 ) + 2( x - 5 ) = ( x - 5 )( 4a + 2 ) = ( x - 5 )2( 2a + 1 )
6. -3a( x - 3 ) + ( 3 - x ) = 3a( 3 - x ) + 1( 3 - x ) = ( 3a + 1 )( 3 - x )
7/ xm+1 - xm = xm( x + 1 )
8/ xm+2 - x2 = x2( xm - 1 )
a) \(a^2+b^2+2ab+2a+2b+1=\left(a^2+2ab+b^2\right)+\left(2a+2b\right)+1\)
\(=\left(a+b\right)^2+2\left(a+b\right)+1=\left[\left(a+b\right)+1\right]^2=\left(a+b+1\right)^2\)
b) K phân tích dc.
\(2\left(a-2b\right)+3a\left(2b-a\right)=2\left(a-2b\right)-3a\left(a-2b\right)=\left(2-3a\right)\left(a-2b\right)\)
\(a\left(m-n\right)-5\left(n-m\right)=a\left(m-n\right)+5\left(m-n\right)=\left(a+5\right)\left(m-n\right)\)
a) Ta có: \(2\left(a-2b\right)+3a\left(2b-a\right)\)
\(=2\left(a-2b\right)-3a\left(a-2b\right)\)
\(=\left(a-2b\right)\left(2-3a\right)\)
b) Ta có: \(a\left(m-n\right)-5\left(n-m\right)\)
\(=a\left(m-n\right)+5\left(m-n\right)\)
\(=\left(m-n\right)\left(a+5\right)\)