Chapter 7.3, Problem 32E

To determine

To describe: Describe the error and correct the following expression :- $(s+5)(s-5)=s^2+2(s)(5)-5^2=s^2+10s-25$ .

Answer to Problem 32E

Incorrect identity is used. Correct expression is $(s+5)(s-5)={(s)}^2-{(5)}^2=s^2-25$ .

Explanation of Solution

Given information: An incorrect expression is given.

Calculation:

Correct algebraic identity is $(a+b)(a-b)=a^2-b^2$ , while in the above expression identity is incorrectly used. Mathematically, $(a+b)(a-b)\ne a^2+2ab-b^2$ .

Applying correct identity,

  $(s+5)(s-5)={(s)}^2-{(5)}^2$

  $=s^2-25$ (Evaluating powers)

Thus, the correct expression is $(s+5)(s-5)=s^2-25$ .