`a) 3x ²y + 6xy` `b) x ²( x – y ) + 2 ( y – x )` `c) x ² – y ² + 6x + 9` `d) x ³ + 3x ² – 4x – 12`

2 bình luận về “`a) 3x ²y + 6xy` `b) x ²( x – y ) + 2 ( y – x )` `c) x ² – y ² + 6x + 9` `d) x ³ + 3x ² – 4x – 12`”

1. a, 3x^2 y + 6xy

   = 3xy . x + 3xy .2

   = 3xy(x + 2)

   b, x^2 (x – y) + 2(y – x)

   = x^2 (x – y) – 2(x – y)

   = (x – y)(x^2- 2)

   = (x – y)(x – \sqrt{2})(x + \sqrt{2})

   c, x^2 – y^2 + 6x + 9

   = (x^2 + 6x +9) – y^2

   = (x + 3)^2 – y^2

   = (x -y  + 3)(x + y+ 3)

   d, x^3 + 3x^2 – 4x – 12

   = x^2 (x +3) – 4(x +3 )

   = (x + 3)(x^2 – 4)

   = (x + 3)(x -2)(x +2 )

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2. Giải đáp:

    

   Lời giải và giải thích chi tiết:

     a) 3x²y + 6xy

   = 3xy ( x + 2 )

   b) x² ( x – y ) + 2 ( y – x )

     = x² ( x – y ) – 2 ( x – y )

   = ( x² – 2 ) ( x – y )

   = ( x + √2 )( x – √2 ) ( x – y )

   c) x² – y² + 6x + 9

   = ( x² + 6x + 9 ) – y²

   = ( x  + 3)² – y²

   = ( x + 3 + y ) ( x + 3 – y )

   d) x³ + 3x² – 4x – 12

   = ( x³ + 3x² ) – ( 4x + 12 )

   = x² ( x + 3 ) – 4 ( x + 3 )

   = ( x² – 4 ) ( x + 3 )

   = ( x + 2 ) ( x – 2 ) ( x + 3 )

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