Algebraic Identity (a-b)2=a2-2ab+b2
Algebraic Identity
(a-b)2=a2-2ab+b2
Example 1
$$\textup{Expand } (x-2)^2 $$
Solution
\begin{align*}
\because\;\;(a-b)^2&=a^2-2ab+b^2\\\\
\therefore\;\; (x-2)^2 &=(x)^2-2(x)(2)+(2)^2\\
&=x^2-4x+4\\
\end{align*}
Example 2
$$\textup{Expand } (m-7)^2 $$
Solution
\begin{align*}
\because\;\;(a-b)^2&=a^2-2ab+b^2\\\\
\therefore\;\; (m-7)^2 &=(m)^2-2(m)(7)+(7)^2\\
&=m^2-14m+49\\
\end{align*}
Example 3
$$\textup{Expand } (3x-5)^2 $$
Solution
\begin{align*}
\because\;\;(a-b)^2&=a^2-2ab+b^2\\\\
\therefore\;\; (3x-5)^2 &=(3x)^2-2(3x)(5)+(5)^2\\
&=9x^2-30x+25\\
\end{align*}
Example 4
$$\textup{Expand } (4y-1)^2 $$
Solution
\begin{align*}
\because\;\;(a-b)^2&=a^2-2ab+b^2\\\\
\therefore\;\; (4y-1)^2 &=(4y)^2-2(4y)(1)+(1)^2\\
&=16y^2-8y+1\\
\end{align*}