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*}