Chapter 8.7, Problem 1AGP

To determine

To factor: The given polynomial.

Answer to Problem 1AGP

The factored polynomial is $81-c^2=\left(9-c\right)\left(9+c\right)$

Explanation of Solution

Given information:

The given polynomial is $81-c^2$ .

Concept used:

The difference of two squares can be factored as $a^2-b^2=\left(a-b\right)\left(a+b\right)$ .

Calculations:

The given polynomial E (say) is $E=81-c^2$ that can be written as

  $E=9^2-c^2$

  $\Rightarrow E=\left(9-c\right)\left(9+c\right)$ .

Thus, the factored polynomial is $E=81-c^2=\left(9-c\right)\left(9+c\right)$ .

Conclusion:

The factored polynomial is $81-c^2=\left(9-c\right)\left(9+c\right)$ .