Factorization a2-2ab+b2=(a-b)2
Factorization
a2-2ab+b2=(a-b)2
Example 1
$$\textup{Factorize } x^2-4x+4 $$
Solution
\begin{align*}
&\because\;\; a^2-2ab+b^2=(a-b)^2 \\\\
&\therefore\;\; x^2-4x+4 \\
&=(x)^2-2(x)(2)+(2)^2 \\
&=(x-2)^2 \\
\end{align*}
Example 2
$$\textup{Factorize } z^2-10z+25 $$
Solution
\begin{align*}
&\because\;\; a^2-2ab+b^2=(a-b)^2\\\\
&\therefore\;\; z^2-10z+25 \\
&=(z)^2-2(z)(5)+(5)^2 \\
&=(z-5)^2 \\
\end{align*}
Example 3
$$\textup{Factorize } 9x^2-24x+16 $$
Solution
\begin{align*}
&\because\;\; a^2-2ab+b^2=(a-b)^2 \\\\
&\therefore\;\; 9x^2-24x+16 \\
&=(3x)^2-2(3x)(4)+(4)^2 \\
&=(3x-4)^2 \\
\end{align*}
Example 4
$$\textup{Factorize } 4y^2-20y+25 $$
Solution
\begin{align*}
&\because\;\; a^2-2ab+b^2=(a-b)^2\\\\
&\therefore\;\; 4y^2-20y+25 \\
&=(2y)^2-2(2y)(5)+(5)^2 \\
&=(2y-5)^2 \\
\end{align*}