Question

Find the value of c that makes the expression a perfect square trinomial.

x2 + 4x + c

Answer 1

the value of c that makes the expression a perfect square binomial is c=4 .

Step-by-step explanation:

Here we have , an expression x2 + 4x + c or , $x^2 + 4x + c$ . We need to find  the value of c that makes the expression a perfect square binomial. Let's find out:

We have ,  $x^2 + 4x + c$

⇒ $x^2+4x+c$

⇒ $x^2+2(2)x+c$

Now , we know that $(a+b)^2=a^2+2(a)(b)+b^2$

Comparing above equation  , to  $x^2+2(2)x+c$ we get ;

⇒  $x^2+2(2)x+c$            { $c=2^2$  }

⇒  $x^2+2(2)x+2^2$

⇒  $(x+2)^2$

Therefore , the value of c that makes the expression a perfect square binomial is c=4 .