Algebraic Identity (a-b)3=a3-3a2b+3ab2-b3
Algebraic Identity
(a-b)3=a3-3a2b+3ab2-b3
Example 1
$$\textup{Expand } (x-2)^3 $$
Solution
\begin{align*}
\because\;\;(a-b)^3&=a^3-3a^2b+3ab^2-b^3\\\\
\therefore\;\; (x-2)^3&=(x)^3-3(x)^2(2)+3(x)(2)^2-(2)^3\\
&=x^3-3(x^2)(2)+3(x)(4)-8\\
&=x^3-6x^2+12x-8\\
\end{align*}
Example 2
$$\textup{Expand } (y-1)^3 $$
Solution
\begin{align*}
\because\;\;(a-b)^3&=a^3-3a^2b+3ab^2-b^3\\\\
\therefore\;\; (y-1)^3&=(y)^3-3(y)^2(1)+3(y)(1)^2-(1)^3\\
&=y^3-3(y^2)(1)+3(y)(1)-1\\
&=y^3-3y^2+3y-1\\
\end{align*}