Chapter 9, Problem 11QC

To determine

Determine the trinomial $x^2+20x+100$ is a perfect square or not.

Answer to Problem 11QC

Yes, it is a perfect square. ${(x+10)}^2$

Explanation of Solution

Given:

The trinomial: $x^2+20x+100$

Concept Used:

Rule for perfect square term: ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

Rule for perfect square term: ${(a+b)}^2=a^2+2ab+b^2$

The first term is a perfect square. $x^2={(x)}^2$

The last term is a perfect square. $100={10}^2$

If the middle term is equal to 2ab: $20x=2·x·10$ then it is a perfect square.

So, $x^2+20x+100$ is a perfect square trinomial.

  $x^2+20x+100={(x)}^2+2·x·10+{10}^2={(x+10)}^2$

Thus, yes, it is a perfect square. $x^2+20x+100={(x+10)}^2$