Question

5 find the product. (c + d)(c - d) p. $c^2 - 2cd + d^2$ q. $c^2 + 2cd + d^2$ r. $c^2 - d^2$ s. $c^2 + d^2$

Explanation:

Step1: Apply the distributive property (FOIL method)

To find the product of \((c + d)(c - d)\), we use the distributive property (also known as the FOIL method for binomials). The formula for the product of a sum and a difference of two terms is \((a + b)(a - b)=a^2 - b^2\). Here, \(a = c\) and \(b = d\).

Expanding \((c + d)(c - d)\) using the distributive property:
\[

$$\begin{align*} (c + d)(c - d)&=c\times c - c\times d + d\times c - d\times d\\ &=c^2 - cd + cd - d^2 \end{align*}$$

\]

Step2: Simplify the expression

The middle terms \(-cd\) and \(+cd\) cancel each other out:
\[
c^2 - cd + cd - d^2 = c^2 - d^2
\]

Answer:

R. \(c^2 - d^2\)