# How do you write an equation for the terms in an answer for a squared polynomial with x terms?

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For example #(a+b)^2 = a^2+2ab+b^2# the polynomial has two terms, the squared answer has 3 terms

along with the pattern #(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2cb# the polynomial has three terms and the squared answer has 6.

and the pattern keeps going. How do I write an equation to show if x terms in polynomial then y terms in answer?

so #(a+b+c+d.......)^2= x# number of terms

For example

along with the pattern

and the pattern keeps going. How do I write an equation to show if x terms in polynomial then y terms in answer?

so

##### 1 Answer

#### Explanation:

The total number of terms on the right hand side is:

#n+1/2(n^2-n) = 1/2(n^2+n)#

Essentially the number of terms on the right hand side is