Chapter 8.7, Problem 41P

Factor each expression.

$41.45s^2-210s+245$

To determine

To factor the expression $45s^2-210w+245$

Answer to Problem 41P

The factors of the given expression are $5\left(3s-7\right)\left(3s-7\right)$ .

Explanation of Solution

Given information:

Given expression $45s^2-210w+245$

  $\begin{array}{l}\text{Given}45s^2-210w+245=5\left(9s^2-42w+49\right)\\ =5\left({\left(3s\right)}^2-2\left(3s\right)\left(7\right)+{\left(7\right)}^2\right)\end{array}$

As we know that $a^2-2ab+b^2={\left(a-b\right)}^2$

Put $a=3s,b=7$ , we get $\left({\left(3s\right)}^2-2\left(3s\right)\left(7\right)+{\left(7\right)}^2\right)={\left(3s-7\right)}^2$

Multiplying $5$ on both sides, we get

  $\begin{array}{l}5\left({\left(3s\right)}^2-2\left(3s\right)\left(7\right)+{\left(7\right)}^2\right)={\left(3s-7\right)}^2\\ =5\left(3s-7\right)\left(3s-7\right)\end{array}$

Hence, the factors of the given expression are $5\left(3s-7\right)\left(3s-7\right)$ .