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9(a + b)2 - (a + b) = (a + b)[9(a + b) - 1]
(mx + my) + (3x + 3y) = m(x + y) + 3(x + y) = (m + 3)(x + y)
(12xy) - 6x - (2y - 1) = 6x(2y - 1) - (2y - 1) = (6x - 1)(2y - 1)
(7xy2 - 5x2y) + (5x - 7y) = xy(7y - 5x) + (5x - 7y) = -xy(5x - 7y) + (5x - 7y) = (-xy + 1)(5x - 7y)
2x(x - y) - (4x - 4y) = 2x(x - y) - 4(x - y) = (2x - 4)(x - y)
a) 9( a + b )2 - ( a + b ) = ( a + b )[ 9( a + b ) - 1 ]
b) ( mx + my ) + ( 3x + 3y ) = m( x + y ) + 3( x + y ) = ( m + 3 )( x + y )
c) 12xy - 6x - ( 2y - 1 ) = 6x( 2y - 1 ) - ( 2y - 1 ) = ( 6x - 1 )( 2y - 1 )
d) ( 7xy2 - 5x2y ) + ( 5x - 7y ) = xy( 7y - 5x ) + ( 5x - 7y ) = -xy( 5x - 7y ) + ( 5x - 7y ) = ( -xy + 1 )( 5x - 7y )
e) 2x( x - y ) - ( 4x - 4y ) = 2x( x - y ) - 4( x - y ) = ( 2x - 4 )( x - y )
\(\left(a-b\right)^2-\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b+1\right)\)
\(5\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)\)
\(=\left(a+b\right)\left[5\left(a+b\right)-\left(a-b\right)\right]\)
\(=\left(a+b\right)\left[5a+5b-a+b\right]\)
\(=\left(a+b\right)\left[4a+6b\right]\)
\(a,\left(a+b\right)+\left(a+b\right)^2\)
\(=\left(a+b\right)\left(1+a+b\right)\)
\(b,4\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\left(4+3\left(x-y\right)\right)\)
\(=\left(x-y\right)\left(4+3x-3y\right)\)
\(c,\left(a-b\right)+\left(b-a\right)^2\)
\(=\left(a-b\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(1+a-b\right)\)
a) \(\left(a+b\right)+\left(a+b\right)^2=\left(a+b\right)\left(1+a+b\right)\)
b) \(4\left(x-y\right)+3\left(x-y\right)^2=\left(x-y\right)\left[4+3.\left(x-y\right)\right]\)
c) \(\left(a-b\right)+\left(b-a\right)^2=\left(a-b\right)+\left(b-a\right)\left(b-a\right)\)
\(=\left(a-b\right)-\left(a-b\right)\left(b-a\right)\)
\(=\left(a-b\right)\left(1-b+a\right)\)
d) \(\left(a-b\right)-\left(b-a\right)^2\)
\(=\left(a-b\right)-\left(b-a\right)\left(b-a\right)\)
\(=\left(a-b\right)+\left(a-b\right)\left(b-a\right)\)
\(=\left(a-b\right)\left(1+b-a\right)\)
e) \(a\left(a-b\right)^2-\left(b-a\right)^3\)
\(=a\left(a-b\right)-\left(a-b\right)\left(b-a\right)^2\)
\(=\left(a-b\right)\left[a-\left(b-a\right)^2\right]\)
f) \(\left(y+z\right)\left(12x^2+6x\right)+\left(y-z\right)\left(12x^2+6x\right)\)
\(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)
\(=\left(12x^2+6x\right)2y\)
a)\(A=\left(x^2-2x\right)\left(x^2-2x-1\right)-6=\left(x^2-2x\right)^2-\left(x^2-2x\right)-6\)
\(=\left(x^2-2x+2\right)\left(x^2-2x+3\right)\)
\(5x.\left(x-10\right)-2x+2x+20\)
\(=5x^2-50x+20\)
\(=5\left(x^2-10x+5^2-21\right)\)
\(=5\left[\left(x-5\right)^2-\left(\sqrt{21}\right)^2\right]\)
\(=5\left(x-5-\sqrt{21}\right)\left(x-5+\sqrt{21}\right)\)
\(a\left(a-b\right)^2\left(a+b\right)-\left(b-a\right)^2\left(a^2-5ab+b^2\right)\)
\(=a\left(a-b\right)^2\left(a+b\right)-\left(a-b\right)^2\left(a^2-5ab+b^2\right)\)
\(=\left(a-b\right)^2\left[a.\left(a+b\right)-a^2+5ab-b^2\right]\)
\(=\left(a-b\right)^2\left[a^2+ab-a^2+5ab-b^2\right]\)
\(=\left(a-b\right)^2\left(6ab-b^2\right)\)
Sửa đề: \(\left(a-b\right)^2-\left(b-a\right)\left(a-3b\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\left(a-3b\right)\)
\(=\left(a-b\right)\left(a-b+a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2.\left(a-b\right)\left(a-2b\right)\)
Tham khảo nhé~