Chapter 8.7, Problem 11PPE

To determine

The solution of the given expression.

Answer to Problem 11PPE

The factor of expression $d^2-20d+100$ is $\left(d-10\right)\left(d-10\right)$

Explanation of Solution

Given information:

The expression $d^2-20d+100$

Concept and Formula Used:

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

Calculation:

The given expression is $d^2-20d+100$

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

  $d^2-20d+100={\left(d\right)}^2-2\times d\times 10+{\left(10\right)}^2$

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

Therefore

  $\begin{array}{l}{d}^2-20d+100={\left(d-10\right)}^2\\ d^2-20d+100=\left(d-10\right)\left(d-10\right)\end{array}$

Conclusion:

The factor of expression $d^2-20d+100$ is $\left(d-10\right)\left(d-10\right)$