Chapter 1.4, Problem 31E

Solution

To describe: The error in the given factoring and then correct it.

The error was at taking out the common factor 4, and the correct factorization is $4(x+3)(x-3)$ .

Given information:

The factoring as shown below.

  $\begin{array}{c}4x^2-36=4\left(x^2-36\right)\\ =4(x+6)(x-6)\end{array}$

Concept used:

Difference of squares formula: $x^2-y^2=\left(x+y\right)\left(x-y\right)$

Error description:

The error in the given calculation is at the first step while taking out the common factor 4.

After taking out the common factor 4, the expression should be written as $4\left(x^2-9\right)$ .

Calculation:

Factor the expression $4x^2-36$ by first factoring out the common factor 4 and then apply difference of squares formula as follows:

  $\begin{array}{c}4x^2-36=4\left(x^2-9\right)\\ =4\left(x^2-3^2\right)\\ =4(x+3)(x-3)\end{array}$

Conclusion:

The error was at taking out the common factor 4, and the correct factorization is $4(x+3)(x-3)$ .