Sure! Let's simplify the expression [tex]\((3x + 8)(3x - 8)\)[/tex] step by step.
1. Identify the structure of the expression: Notice that [tex]\((3x + 8)(3x - 8)\)[/tex] is in the form of [tex]\((a + b)(a - b)\)[/tex], which is a difference of squares.
2. Apply the difference of squares formula: The difference of squares formula states that [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex]. In our case, [tex]\(a = 3x\)[/tex] and [tex]\(b = 8\)[/tex].
3. Square the terms individually:
- [tex]\(a^2 = (3x)^2 = 9x^2\)[/tex]
- [tex]\(b^2 = 8^2 = 64\)[/tex]
4. Subtract the squared terms:
[tex]\[ 9x^2 - 64 \][/tex]
So, the simplified form of [tex]\((3x + 8)(3x - 8)\)[/tex] is [tex]\(9x^2 - 64\)[/tex].
Thus, we have:
[tex]\[ (3x + 8)(3x - 8) = 9x^2 - 64 \][/tex]
