Question

Which way is correct? or both?
(4x^2 -9y^2)=0 into xy(4x-9y)=0 or (2x+3y)(2x-3y)=0

Answer 1

4 x² - 9 y² = 0

Rewrite this expresion as:

( 2 x )² - ( 3 y )² = 0

So:

4 x² - 9 y² = ( 2 x )² - ( 3 y )² = 0

Apply the difference of two squares formula:

a² - b² = ( a + b ) ( a - b )

In this case:

( 2 x )² - ( 3 y )² = 0

( 2 x + 3 y ) ( 2 x - 3 y ) = 0

Answer 2

Correct is:

( 2 x + 3 y ) ( 2 x - 3 y ) = 0

because:

x y ( 4 x - 9 y ) = y ∙ ( 4 x ∙ x - 9 y ∙ x ) = y ∙ ( 4 x² - 9 x y )

That is not your expression:

4 x² - 9 y²

Answer 3

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