Chapter 8.7, Problem 10PPE

To determine

The solution of the given expression.

Answer to Problem 10PPE

The factor of expression $v^2-10v+25$ is $\left(v-5\right)\left(v-5\right)$

Explanation of Solution

Given information:

The expression $v^2-10v+25$

Concept and Formula Used:

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

Calculation:

The given expression is $v^2-10v+25$

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

  $v^2-10v+25={\left(v\right)}^2-2\times 5\times v+{\left(5\right)}^2$

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

Therefore

  $\begin{array}{l}{v}^2-10v+25={\left(v-5\right)}^2\\ v^2-10v+25=\left(v-5\right)\left(v-5\right)\end{array}$

Conclusion:

The factor of expression $v^2-10v+25$ is $\left(v-5\right)\left(v-5\right)$