Absolutely, let's factorize the given expression [tex]\( x^2 - 16 \)[/tex].
1. Recognize the form of the expression: The given expression [tex]\( x^2 - 16 \)[/tex] is a difference of squares.
The difference of squares formula is given by:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
2. Identify the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]: In this formula, [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the square roots of the terms in the expression.
- For [tex]\( x^2 \)[/tex], the square root is [tex]\( x \)[/tex]. Therefore, [tex]\( a = x \)[/tex].
- For [tex]\( 16 \)[/tex], the square root is [tex]\( 4 \)[/tex]. Therefore, [tex]\( b = 4 \)[/tex].
3. Apply the difference of squares formula: Substitute [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula.
[tex]\[
x^2 - 16 = x^2 - 4^2 = (x - 4)(x + 4)
\][/tex]
So, the factorized form of [tex]\( x^2 - 16 \)[/tex] is:
[tex]\[
(x - 4)(x + 4)
\][/tex]
This is the fully factorized expression for [tex]\( x^2 - 16 \)[/tex].
