To multiply the two binomials \((6x - 7)(6x + 7)\), we can use the distributive property (also known as the FOIL method for binomials):
\[ (6x - 7)(6x + 7) = 6x \cdot 6x + 6x \cdot 7 - 7 \cdot 6x - 7 \cdot 7 \]
Calculating each part:
- \(6x \cdot 6x = 36x^2\)
- \(6x \cdot 7 = 42x\)
- \(-7 \cdot 6x = -42x\)
- \(-7 \cdot 7 = -49\)
Now, combining all these terms together:
\[ 36x^2 + 42x - 42x - 49 \]
The \(42x\) and \(-42x\) cancel each other out:
\[ 36x^2 - 49 \]
So, the final answer in standard form is:
\[ \boxed{36x^2 - 49} \]