Question

factorise the expression 9x^2y^2 - 16​

Answer 1

Answer...

Refers to the attachment

Answer 2

♠ Step-by-step explanation:

Final result :

 (3xy + 4) • (3xy - 4)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (32x2 • y2) -  16

Step  2  :

Trying to factor as a Difference of Squares :

2.1      Factoring:  9x2y2-16  

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 : 16 is the square of 4

Check :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

Factorization is :       (3xy + 4)  •  (3xy - 4)  

Final result :

 (3xy + 4) • (3xy - 4)