I need help with the following problem

Question

1) 2x^2-3x=-1

2) (x-5)(x+2)=8

3) 4x^2-9/8x^3-27

4) 3x^2-7xy+2y/12x^2+11xy-5y^2/5x-10y/16x^2+40xy+25y^2

Answer 1

1)

2x² - 3x = -1

2x² - 3x +1 = 0

2x² - 2x –x +1 = 0

2x ( x – 1) –1( x -1 ) = 0

( x – 1) ( 2x –1 ) = 0

Solution : Factorized Form is   ( x – 1) ( 2x –1 ) = 0.

Answer 2

2)

( x - 5 ) ( x + 2 ) = 8

x ( x + 2 ) - 5 ( x + 2 ) = 8

x² + 2x - 5x - 10 = 8

x² - 3x - 10 - 8 = 0

x² - 3x - 18 = 0

x² - 6x + 3x - 18 = 0

x ( x – 6) – 3( x - 6 ) = 0

(x - 6) ( x - 3 ) = 0

Solution : Factorized Form is   ( x – 6) ( x –3 ) = 0.

Answer 3

3) Given function

Apply formulas :

 

Answer 4

4) Given function is

 

 

Now factorize all expressions separately

    

    

 

    

  

 

   

    

 

Solution : (1/5)(x+5y).