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Answer:
You didn't mention if it is to simplify or to factorize. So have done both.
Step-by-step explanation:
[tex]If \ a = \frac{1}{3}x \ , \ b = \frac{2}{5}y , \ then \ the \ expression \ is \ of \ the \ form \ a^2 - 2ab + b^2[/tex] [tex]which \ is \ (a - b)^2[/tex].
So if you want to expand :
[tex](\frac{1}{3}x)^2 - 2 (\frac{1 \times x}{3})(\frac{2 \times y}{5}) + (\frac{2}{5}y)^2[/tex] [tex]=\frac{x^2}{9} - \frac{4xy}{15} + \frac{4y^2}{25}[/tex]
If it is to factorize :
[tex](\frac{1}{3}x)^2 - 2 (\frac{1 \times x}{3})(\frac{2 \times y}{5}) + (\frac{2}{5}y)^2 = (\frac{1}{3}x-\frac{2}{5}y)(\frac{1}{3}x - \frac{2}{5}y)=(\frac{1}{3}x - \frac{2}{5}y)^2[/tex]