Algebraic Identity (a+b)(a-b)=a2-b2
Algebraic Identity
(a+b)(a-b)=a2-b2
Example 1
$$\textup{Expand } (x+3)(x-3) $$
Solution
\begin{align*}
\because\;\;(a+b)(a-b)&=a^2-b^2\\\\
\therefore\;\; (x+3)(x-3) &=(x)^2-(3)^2\\
&=x^2-9\\
\end{align*}
Example 2
$$\textup{Expand } (y+4)(y-4) $$
Solution
\begin{align*}
\because\;\;(a+b)(a-b)&=a^2-b^2\\\\
\therefore\;\; (y+4)(y-4) &=(y)^2-(4)^2\\
&=y^2-16\\
\end{align*}
Example 3
$$\textup{Expand } (y-2)(y+2) $$
Solution
\begin{align*}
\because\;\;(a-b)(a+b)&=a^2-b^2\\\\
\therefore\;\; (y-2)(y+2) &=(y)^2-(2)^2\\
&=y^2-4\\
\end{align*}
Example 4
$$\textup{Expand } (z-5)(z+5) $$
Solution
\begin{align*}
\because\;\;(a-b)(a+b)&=a^2-b^2\\\\
\therefore\;\; (z-5)(z+5) &=(z)^2-(5)^2\\
&=z^2-25\\
\end{align*}