Bài 1 : ( x + 3 ) ² = x² + 2.x.3 + 3² = x² + 6x + 9 ( 2x + 1 ) ² = ( 2x ) ² + 2.2x.1 +1² = 4x² + 4x +1 ( 4x - 5 ) ² = ( 4x ) ² - 2.4x.5 + 5² = 16x² - 40x + 25 ( x - 1/2 ) ² = x² - 2.x.1/2 + (1/2)² = x² - x + 1/4 ( 1 - 5a )² = 1² - 2.1.5a + ( 5a ) ² = 1 - 10a + 25a² x² - 4 = x² - 2² = ( x - 2 ) ( x + 2 ) 4a² - 9 = ( 2a )² - 3² = ( 2a - 3 ) ( 2a + 3 ) 25 - 100b² = 5² - ( 10b ) ² = ( 5 - 10b ) ( 5 + 10b ) ( x + 1 ) ² - y² = ( x + 1 - y ) ( x + 1 + y ) ( x + y ) ² - 25² = ( x + y - 25 ) ( x + y + 25 ) 9y² - ( x + y ) ² = ( 3y ) ² - ( x + y ) ² = [ 3y - ( x + y ) ] ( 3y + x + y ) = ( 3y - x - y ) ( 3y + x + y ) = ( 2y - x ) ( 4y + x ) ( x - 3 ) ( x + 3 ) = x.x + x.3 - 3.x - 3.3 = x² + 3x - 3x - 9 = x² - 9 ( 5x + 1 ) ( 5x - 1 ) = 5x.5x - 5x.1 + 1.5x - 1.1 = 25x² - 5x + 5x - 1 = 25x² - 1 ( 1x/2 - 2y ) ( 1x/2 + 2y ) = x/2 . x/2 + x/2 . 2y - 2y . x/2 - 2y . 2y = x²/4 + 2xy/2 - 2xy/2 - 4y² = x²/4 - 4y² ( 2x/3 + 3y ) ( 3y - 2x/3 ) = 2x/3 . 3y - 2x/3 . 2x/3 + 3y . 3y - 3y . 2x/3 = 6xy/3 - 4x²/9 + 9y² - 6xy/3 = -4x² + 9y² ( 3xy + 2y² ) ( 3xy - 2y² ) = 3xy . 3xy - 3xy . 2y² + 2y² . 3xy - 2y² . 2y² = 9x²y² - 6xy³ + 6xy³ - 4y⁴ = 9x²y² - 4y⁴ ( x + 4 ) ( 4 - x ) = x.4 - x.x + 4.4 - 4.x = 4x - x² + 16 - 4x = - x² + 16 ( 5 - y² ) ( y² + 5 ) = 5.y² + 5.5 - y².y² - y².5 = 5y² + 25 - y⁴ - 5y² = 25 - y⁴ ( a + b + c ) ( a + b - c ) = a.a + a.b - a.c + b.a + b.b + b.c + c.a + c.b - c.c = a² + ab + ac + ab + b² + bc + ac + bc - c² = a² + b² - c² + 2ab + 2bc + 2ac ( a - b + c ) ( a - b - c ) = a.a - a.b - a.c - b.a + b.b + b.c + c.a - a.b - c.c = a² -ab - ac - ab + b² + bc + ac - ab - c² = a² + b² - c² - 3ab + bc ( 2a + 3b + 4c ) ( 2a + 3b - 4c ) = 2a.2a + 2a.3b - 2a.4c + 3b.2a + 3b.3b - 3b.4c + 4c.2a + 4c.3b - 4c.4c = 4a² + 6ab - 8ac + 6ab + 9b² - 12bc + 8ac + 12bc - 16c² = 4a² + 9b² - 16c² + 12ab ( 2x - 1 ) ( 2x + 1 ) ( 4x³ + 1 ) = ( 2x.2x +2x.1 - 1.2x - 1.1 ) ( 4x³ + 1 ) = ( 4x² + 2x - 2x -1 ) ( 4x³ + 1 ) = ( 4x² - 1) ( 4x³ + 1 ) = 4x².4x³ + 4x². 1 - 1.4x³ - 1.1 = 16x⁵ + 4x² - 4x³ - 1 Bài 2 : 1) x² + 2x + 1 = x² + 2.x.1 + 1² = ( x + 1 ) ² 2) 25 + 10x + x² =x² + 10x + 2 5= x² + 2.x.5 + 5² = ( x + 5 )² 3) 9 - 6x + x² = x² - 6x + 9= x² - 2.x.3 + 3² = ( x - 3 ) ² 4) x² - x + 1/ 4= x² - 2.x.1/2 + ( 1/2)² = ( x - 1/ 2) ² 5) 4x² + 1- 4x = 4x² - 4x + 1= ( 2x ) ² - 2.2x. 1+ 1² = ( 2x - 1) ² 6) -12xy + 9y² + 4x² = 4x² - 12xy + 9y² = ( 2x ) ² + 2. 2x .3y + ( 3y ) ² = ( 2x + 3y ) ² 7) 9a² - 6a + 1 = ( 3a ) ² - 2.3a. 1+ 1² = ( 3a -1 ) ² 8) y² - 12y + 16= y² - 2.y.6 + 6² - 20 = ( y - 6 ) ² - 20 9) x² +4x + 4 = x² + 2.x.2 + 2² = ( x + 2) ² 10) 4m² - 12mn + 9n² = ( 2m ) ² - 2.2m.3n + ( 3n ) ² = ( 2m - 3n ) ² 11) z² + 20xz + 100x² = z² + 2.z.10x + ( 10x ) ² = ( z + 10x )² 12) x⁴ - 12x² + 36 = ( x ² ) ² - 2.x².6 + 6² = ( x² - 6 ) ²