Question

polynomial arithmetic and structure: tutorial question enter the correct answer in the box. use the difference of squares identity to write this polynomial expression in factored form: 9x² - 49.

Explanation:

Step1: Recall the difference of squares identity

The difference of squares identity is $a^2 - b^2=(a + b)(a - b)$.

Step2: Identify \(a\) and \(b\) in the given polynomial

For the polynomial \(9x^2-49\), we can rewrite \(9x^2\) as \((3x)^2\) and \(49\) as \(7^2\). So, \(a = 3x\) and \(b=7\).

Step3: Apply the difference of squares identity

Substitute \(a = 3x\) and \(b = 7\) into the identity \(a^2 - b^2=(a + b)(a - b)\). We get \((3x)^2-7^2=(3x + 7)(3x - 7)\).

Answer:

\((3x + 7)(3x - 7)\)