Homework Help

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

user profile pic

xav1394 | Student, Grade 11 | (Level 2) eNoter

Posted November 26, 2011 at 6:45 PM via web

dislike 0 like

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

2 Answers | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 26, 2011 at 6:59 PM (Answer #1)

dislike 0 like

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` .

user profile pic

kashmirinnocence | Student, Undergraduate | (Level 1) Honors

Posted November 26, 2011 at 10:28 PM (Answer #2)

dislike 0 like

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