prove the trinomial x^2+2x+1 is binomial squared

### 2 Answers | Add Yours

You need to remember the formula of the perfect square:

(a+b)^2=a^2 + 2ab + b^2

Compare the trinomial and the expansion of binomial raised to square.

`x^2 + 2x + 1 = a^2 + 2ab + b^2`

Take a look at both expansions and you'll conclude that a=x and b=1.

Based on this conclusion, you may write the trinomial as a binomial raised to square.

`x^2 + 2x + 1 = (x+1)^2`

**ANSWER: The trinomial `x^2 + 2x + 1` is the expansion of binomial `(x+1)^2` .**

x^2+2x+1=x^2+x+x+1{splitting yhe middle term}

=x(x+1)+1(x+1){taking common out}

=(x+1)(x+1)

=(x+1)^2 which implies:

x^2+2x+1=binomial squared i.e,(x+1)^2

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes