Question

please help it’s due in 35 minutes thanks if you do!!

Answer 1

`n^2 + (2n)/(3) + (1)/(9) = (1)/(9)` --- Trinomial

`(n + (1)/(3))^2 = (1)/(9)` --- Binomial

Explanation:

Given

`n^2 + (2n)/(3)`

Solving (a): Perfect square trinomial

We have:

`n^2 + (2n)/(3)`

Express as an equation

`n^2 + (2n)/(3) =`

Start----------------------------

Take coefficient of n i.e. (2/3)

Half it: i.e. (1/3)

Square it: (1/63^2

Add to both sides of the equation

---------------------------End

So, we have:

`n^2 + (2n)/(3) + ((1)/(3))^2 = ((1)/(3))^2`

Remove brackets

`n^2 + (2n)/(3) + (1)/(9) = (1)/(9)`

Solving (b): Binomial Squared

`n^2 + (2n)/(3) + (1)/(9) = (1)/(9)`

Expand

`n^2 + (n)/(3)+ (n)/(3) + (1)/(9) = (1)/(9)`

Factorize:

`n(n + (1)/(3))+ (1)/(3)(n + (1)/(3)) = (1)/(9)`

Factor out n + 1/3

`(n + (1)/(3))(n + (1)/(3)) = (1)/(9)`

Express as square

`(n + (1)/(3))^2 = (1)/(9)`