Question

Factorize the following expression:
X^3y/9-XY^3/16

Answer 1

Answer:

xy • (x + 3y) • (x - 3y)

Step-by-step explanation:

((x3) • y) - 32xy3

x3y - 9xy3  =   xy • (x2 - 9y2)

 x3y - 9xy3  =   xy • (x2 - 9y2)

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 : 9 is the square of 3

Check :  x2  is the square of  x1 

Check :  y2  is the square of  y1 

Factorization is :       (x + 3y)  •  (x - 3y) 

Final result :

xy • (x + 3y) • (x - 3y)