Chapter 8.4, Problem 25P

Mental Math Simplify each product.

$25.{89}^2$

To determine

To simplify: The product ${89}^2$ .

Answer to Problem 25P

  $\text{7921}$

Explanation of Solution

Given information:

The product to be simplified is ${89}^2$ .

Calculation:

Write the product in the form of ${\left(a-b\right)}^2$ and then apply the formula: ${\left(a-b\right)}^2=a^2-2ab+b^2$ .

  $\begin{array}{c}{89}^2={\left(90-1\right)}^2\\ ={90}^2-2\left(90\right)\left(1\right)+1^2\\ =8100-180+1\\ =\text{7921}\end{array}$