Question

Find the product. $$(9 x+8)(9 x-8)$$

Short answer

The product of \( (9x + 8)(9x - 8) \) simplifies to \( 81x^2 - 64 \).

Step-by-step solution

- Identify the Binomials

Identify the two binomials in the equation which are \( (9x + 8) \) and \( (9x - 8) \). These binomials are in the format \( a + b \) and \( a - b \) respectively.

- Apply the Difference of Squares Formula

Having identified the binomials as the terms 'a' and 'b' in the formula \( a^2 - b^2 \), we can substitute these terms back into the formula. In this context, 'a' is \( 9x \), and 'b' is \( 8 \). So, using the difference of squares formula, \( (a + b)(a - b) = a^2 - b^2 \), we have \( (9x)^2 - (8)^2 \).

- Simplify the Result

Finally, simplify the equation to its simplest form. Square the terms in the equation to get \( 81x^2 - 64 \).