Question

Divide 81 -x^2 y^2 by (9-xy) (3 + xy)​

Answer 1

When we divide 81 -x²y² by (9-xy) (3 + xy)​, we determine the expression is:

`(81-x^2y^2)/(\left(9-xy\right)\left(3+xy\right))=(9+xy)/(3+xy)`

Explanation:

Let us divide 81 -x²y² by (9-xy) (3 + xy)​

so

Given the expression

`(81-x^2y^2)/(\left(9-xy\right)\left(3+xy\right))`

Factor -x²y² + 81 = (9+xy) (9-xy)

`(81-x^2y^2)/(\left(9-xy\right)\left(3+xy\right))=(\left(9+xy\right)\left(9-xy\right))/(\left(9-xy\right)\left(3+xy\right))`

Cancel the common term: 9-xy

`=(9+xy)/(3+xy)`

Therefore, when we divide 81 -x²y² by (9-xy) (3 + xy)​, we determine the expression is:

`(81-x^2y^2)/(\left(9-xy\right)\left(3+xy\right))=(9+xy)/(3+xy)`