Question

Find the product. $$(b+9)(b-9)$$

Short answer

The product is \( b^2 - 81 \)

Step-by-step solution

Recognize the pattern

The given product \( (b+9)(b-9) \) fits the pattern of \( (a+b)(a-b) \). Here, \( a \) is \( b \) and \( b \) is \( 9 \).

Apply the formula

The formula for the product of two binomials of the form \( (a+b)(a-b) \) is \( a^2 - b^2 \). Substitute \( a = b \) and \( b = 9 \) into the formula to obtain the product.

Substitute and simplify

Substituting into the equation gives \( b^2 - 9^2 \), which simplifies to \( b^2 - 81 \).