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

2 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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 Comments

kashmirinnocence's profile pic

kashmirinnocence | Student, Undergraduate | (Level 1) Honors

Posted on

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

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


=(x+1)^2     which implies:

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