Question

find factors of 12x^3 y^2​

Answer 1

Hey Mate!!

This is the answer

STEP  1 :

Equation at the end of step 1

 12x -  3y2

STEP  2 :

Pulling out like terms

3.1     Pull out like factors :

  12x - 3y2  =   3 • (4x - y2)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  4x - 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 : 4  is the square of  2  

Check :  x1   is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares

Final result :

 3 • (4x - y2)

Hope it helps...

Bye✨