Chapter 8.7, Problem 17PPE

To determine

The solution of the given expression.

Answer to Problem 17PPE

The factor of expression $9n^2-42n+49$ is $\left(3n-7\right)\left(3n-7\right)$

Explanation of Solution

Given information:

The expression $9n^2-42n+49$

Concept and Formula Used:

The property ${\left(a-b\right)}^2=a^2-2ab+b^2$

Calculation:

The given expression is $9n^2-42n+49$

Write the first and last term of the expression as squares and middle term in the form of 2ab

  $9n^2-42n+49={\left(3n\right)}^2-2\times 3n\times 7+{\left(7\right)}^2$

Using the property ${\left(a-b\right)}^2=a^2-2ab+b^2$

Therefore

  $\begin{array}{l}9n^2-42n+49={\left(3n-7\right)}^2\\ 9n^2-42n+49=\left(3n-7\right)\left(3n-7\right)\end{array}$

Conclusion:

The factor of expression $9n^2-42n+49$ is $\left(3n-7\right)\left(3n-7\right)$