Q. 231 - Intermediate Algebra

Question

Explain why $n^2+25\ne {(n+5)}^2$. Use algebra, words, or pictures.

Step-by-Step Solution

Answer

The expansion of ${(n+5)}^2=n^2+10n+25$ and is not equal to $n^2+25$

Step 1. Given information

The given expression is ${(n+5)}^2$

Step 2. Explanation

We will use perfect square trinomial pattern that is using the pattern ${(a+b)}^2$.

Substitute the values in the above pattern and expand,

$$\begin{gathered} {(n+5)}^2={\left(n\right)}^2+2\times n\times 5+{\left(5\right)}^2 \\ =n^2+10n+25 \end{gathered}$$

Thus, we can see that the expansion of the given expression is not equal to $n^2+25$