Chapter 8.7, Problem 40PPE

To determine

To correct the error: in factoring $9x^2-49=\left(9x+7\right)\left(9x-7\right)$

Answer to Problem 40PPE

The correct factor is $9x^2-49=\left(3x+7\right)\left(3x-7\right)$ .

Explanation of Solution

Given Information:The expression is factored as $9x^2-49=\left(9x+7\right)\left(9x-7\right)$ .

Concept used:

Factorize $9x^2-49$ using the formula $a^2-b^2=\left(a+b\right)\left(a-b\right)$

Formula used:

Use the formula $a^2-b^2=\left(a+b\right)\left(a-b\right)$ to factorize $9x^2-49$ .

Calculations:

  $9x^2-49={\left(3x\right)}^2-{\left(7\right)}^2$

The error made in factoring the given expression is that instead of writing $9x^2-49={\left(3x\right)}^2-7^2$ it is written as $9x^2-49={\left(9x\right)}^2-{\left(7\right)}^2$

Result: The correct factors of $9x^2-49$ are calculated using the formula $9x^2-49={\left(3x\right)}^2-{\left(7\right)}^2$

Therefore, $9x^2-49=\left(3x+7\right)\left(3x-7\right)$