Question

1) (a-b)³-3ab(b-a) =

2) (x+1)³ =     (1-x)³ =

3) (3x+2) x (3x-2) + (x+2)² =

4) (3/4x+y)³ x (3/4x-y) =

5) (x-3)²-(x+2)²+(x+3) x (x-1) = 

6) (a-2)² =          (3m-n/5)² =

Answer 1

1) (a-b)³-3ab(b-a) = a³ +3.a².(-b) + 3.a.(-b)² + (-b)³  - 3ab² + 3a²b
     a³ - 3a²b + 3ab² -b³ - 3ab² + 3a²b
     a³  - b³

2) (x+1)³ =   x³ + 3x² + 3a² + 1

3)(1-x)³ =  1³ - 3.1²x + 3.1.x² -x³ ==>  1 - 3x + 3x² - x³

4) (3x+2) x (3x-2) + (x+2)² = 
    9x² - 4 + x² + 4x + 4
     10x² + 4x

5) (3/4x+y)³ x (3/4x-y) =
    
(3/4x)³  + 3.(3/4x)²y + 3.(3/4).x.y²  + y³ ) x (3/4x -y)
27/64x³ +  27/16x²y + 9/4x.y²  + y³ ) x (3/4x -y) 
81/256x^4 + 81/64x³y + 27/16x² + 3/4x -27/64x³y +  27/16x²y² + 9/4x.y³  + y^4

    
6) (x-3)²-(x+2)²+(x+3) x (x-1) = 
    x² - 6x + 9 - x² - 4x - 4 + x² - x + 3x - 3
    x² - 8x + 2

7) (a-2)² =   a² - 4a + 4    

8) (3m-n/5)² =  (3m)² + 2.(3m)(-n/5)  + (-n/5)² 

9m²  - 6m.n/5  + n²/25