Question

Write the expression as a square of a binomial if possible: 1/9 x^2+ 2/15 x y+ 1/25 y^2

Answer 1

Answer:
`\bold{\bigg((1)/(3)x+(1)/(5)y\bigg)^2}`

Explanation:

The square of the trinomial exists only if (a + b)² = a² + 2ab + b²

`(1)/(9)x^2+(2)/(15)xy+(1)/(25)y^2\\\\\\a=\sqrt{(1)/(9)x^2}=(1)/(3)x\\\\\\b=\sqrt{(1)/(25)y^2}=(1)/(5)y\\\\\\2\cdot a\cdot b=2\cdot (1)/(3)x\cdot (1)/(5)y = (2)/(15)xy\\\\\text{So, }(1)/(9)x^2+(2)/(15)xy+(1)/(25)y^2=\bigg((1)/(3)x+(1)/(5)y\bigg)^2\\`