Step-by-step explanation:
[tex] = \frac{1}{9} {x}^{2} + \frac{2}{15} xy + \frac{1}{25} {y}^{2} \\ = \boldsymbol{ \frac{1}{3} {x}^{2} + \frac{1}{5} {y}^{2} }[/tex]
Answer:
[tex] \frac{(x + \frac{3y}{5})^{2} }{9} [/tex]
Step By Step Explanations:
1) Simplify 1/9x² to x²/9.
[tex] \frac{ {x}^{2} }{9} + \frac{2}{15} xy + \frac{1}{25} {y}^{2} [/tex]
2) Simplify 2/15xy to y²/25.
[tex] \frac{ {x}^{2} }{9} + \frac{2xy}{15} + \frac{1}{25} {y}^{2} [/tex]
3) Simplify 1/25y² to y²/25.
[tex] \frac{ {x}^{2} }{9} + \frac{2xy}{15} + \frac{ {y}^{2} }{25} [/tex]
4) Factor with quadratic formula.
[tex] \frac{1}{9} (x + \frac{3y}{5})(x + \frac{3y}{5} )[/tex]
5) use product rule.
[tex] \frac{(x + \frac{3y}{5} )^{2} }{9} [/tex]
Therefor, the answer is (x + 3y/5)²/9.
