Question

Pls help asap!!

Simplify the expression:


(2x−3y)^2
---------------
(3y−2x)^2

Ava simplified the expression and said that the value is -1.


(2x−3y)^2
----------------
(3y−2x)^2


= (2x−3y)^2
-------------------
(−(2x−3y))^2

= (2x−3y)^2
--------------------
−1⋅(2x−3y)^2


= −1



Is Ava's solution correct? If not, find and explain her mistake. Give the correct solution.

Answer 1

Ava method of simplifying the expression was wrong

Ava's mistake is (−(2x−3y))^2 = −1⋅(2x−3y)^2 this was wrong. the square of a negative is positive. (−(2x−3y))^2 = (2x−3y)^2 this is correct

Simplifying with the correct method

(2x - 3y)^2 / (3x - 2y)^2

Simplifying the numerator

= (2x - 3y)^2

= (2x - 3y) * (2x - 3y)

= 4x^2 - 6xy - 6xy + 9y^2

Simplifying the denominator

= (3y - 2x)^2

= (3y - 2x) * (3y - 2x)

= 9y^2  - 6xy - 6xy + 4x^2

rearranging gives

= 4x^2 - 6xy - 6xy + 9y^2

putting together

= (4x^2 - 6xy - 6xy + 9y^2) / (4x^2 - 6xy - 6xy + 9y^2)

= 1

In Ava's method, at this stage (−(2x−3y))^2

(−(2x−3y))^2 = (2x−3y)^2

(−(2x−3y))^2 ≠ −1⋅(2x−3y)^2 -  this was wrong

Learn more on spotting errors in calculation at:

https://brainly.com/question/29420555

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