Question

# $\begin{array} { l r } \text { White } & \text { Black } & \text { Total } \\ & + & ( n + 1 ) ^ { 2 } \end{array}$

Solution

Verified
Step 1
1 of 2

$2n+(n^2+1) =n^2+1$

Using $2n-1$, the number of white dots correspond to the sequence:

$2,4,6,8,\dots$

Using $n^2+1$, the number of black dots correspond to the sequence:

$2,5,10,17,\dots$

which corresponds to sequence $\text{\textcolor{#c34632}{A.}}$

To show that the polynomial addition is true, we notice that $n^2+2n+1$ is a perfect square trinomial: $a^2+2ab+b^2=(a+b)^2$

$2n+n^2+1= n^2+2n+1=\color{#c34632} (n+1)^2\color{white}\tag{1}$

## Recommended textbook solutions

#### enVision Algebra 1

1st EditionISBN: 9780328931576 (2 more)Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek
3,246 solutions

#### SpringBoard Algebra 1

1st EditionISBN: 9781457301513SpringBoard
3,022 solutions

#### Big Ideas Math Algebra 1: A Common Core Curriculum

1st EditionISBN: 9781608408382 (2 more)Boswell, Larson
4,740 solutions

#### Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions