Question

A(3x-2y)+b(2y-3x) factorize

Answer 1

Hope you like my process

°=======================°

=>A(3x-2y)+b(2y-3x)

=> A(3x-2y)-b(3x-2y)

=> (A-b)(3x-2y)_____(answer)

_______________________

=> Factorisations is the form of simply converting an equation into its factors.

Here doing this may give simple and easy solution to critical problems..

____________________

Hope this is ur required answer

Proud to help u

Answer 2

Step by step solution :

Step  1  :

 1.1    Evaluate :  (3x-2y)2   =  9x2-12xy+4y2   1.2    Evaluate :  (2x-3y)2   =  4x2-12xy+9y2 

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   5x2 - 5y2  =   5 • (x2 - y2) 

Trying to factor as a Difference of Squares :

 2.2      Factoring:  x2 - y2 

Theory : A difference of two perfect squares, A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  x2  is the square of  x1 

Check :  y2  is the square of  y1 

Factorization is :       (x + y)  •  (x - y) 

Final result :

5 • (x + y) • (x - y)