How do I factor #16/25x^2y^2-36/49y^4#?

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Answer 1 · 2018-02-20T23:05:12

See a solution process below:

This is a special form of the quadratic:

#color(red)(a)^2 - color(blue)(b)^2 = (color(red)(a) + color(blue)(b))(color(red)(a) - color(blue)(b))#

If we let:

#color(red)(a)^2 = 16/25x^2y^2#

Then:

#sqrt(color(red)(a)^2) = sqrt(16/25x^2y^2)#

#color(red)(a) = 4/5xy#

And, we let:

#color(blue)(b)^2 = 36/49y^4#

Then:

#sqrt(color(blue)(b)^2) = sqrt(36/49y^4)#

#color(blue)(b) = 6/7y^2)#

Substituting into the formula above gives:

#16/25x^2y^2 - 36/49y^4 = (4/5xy + 6/7y^2)(4/5xy - 6/7y^2)#