Question

When a product is raised to a power, it is equal to the product of each factor raised to that power. Show that this rule does not apply for a sum or difference to a power using the problem (5 – 3)2. You may indicate an exponent in your answer with ^. For example, 3x2 as 3x^2.

Answer 1

Here are two ways of showing the value of the given expression:\[\begin{align*}
(5-3)^2&=2^2\\
&=4
\end{align*}\]
\[\begin{align*}
(5-3)^2&=(5-3)(5-3)\\
&=5(5-3)-3(5-3)&\text{distributive property}\\
&=25-15-15+9&\text{dist prop}\\
&=4
\end{align*}\]
Meanwhile, you have
\[\begin{align*}
(5-3)^2&\not=5^2-3^2\\
&=25-9\\
&=16\not=4
\end{align*}\]