Chapter 8, Problem 9SGR

To determine

To state whether the statement is true or false

Answer to Problem 9SGR

False

Explanation of Solution

Given:

Statement: $x^2-16$ is an example of perfect square trinomial.

Concept used:

Difference of squares: $a^2-b^2=(a+b)(a-b)$

Perfect square trinomials have three terms and they are of the form ${(a+b)}^2.$

Calculation:

Consider the given expression,

  $\Rightarrow x^2-16$

On observing the expression, there are only two terms which is a binomial. A trinomial has three terms. Therefore, it cannot be a perfect square trinomial.

On simplifying the polynomial,

  $x^2-16=({(x)}^2-4^2)=(x-4)(x+4)$

The given statement can be true if it is a difference of squares.

Conclusion:

Therefore, $x^2-16$ is not an example of perfect square trinomial.