Certainly! Let's look at how we can approach the given expression step-by-step.
Step 1: Write down the given expression
The given expression is:
[tex]\[ x^2 - 9 \][/tex]
Step 2: Recognize the form of the expression
Notice that the expression [tex]\( x^2 - 9 \)[/tex] is a difference of squares. The difference of squares formula is given by:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In this case, [tex]\( a = x \)[/tex] and [tex]\( b = 3 \)[/tex]. So we can rewrite [tex]\( x^2 - 9 \)[/tex] as:
[tex]\[ x^2 - 9 = x^2 - 3^2 \][/tex]
Step 3: Apply the difference of squares formula
Substitute [tex]\( a = x \)[/tex] and [tex]\( b = 3 \)[/tex] into the difference of squares formula:
[tex]\[ x^2 - 3^2 = (x - 3)(x + 3) \][/tex]
Step 4: Write the final simplified expression
Thus, the simplified form of the expression [tex]\( x^2 - 9 \)[/tex] is:
[tex]\[ x^2 - 9 = (x - 3)(x + 3) \][/tex]
This is the factorized form of the given polynomial.
