Question

write a multiplication expression to represent each model.
13
there are 4 rows of tiles.
each row represents x + x + x + 1, or 3x + 1.
4(3x + 1)
14
15
16
17
18

Explanation:

Problem 14

Step1: Analyze the model

There are 2 rows of tiles. Each row represents \( x + 1 + 1 + 1 \), or \( x + 3 \).

Step2: Write the multiplication expression

To represent 2 rows of \( x + 3 \), the multiplication expression is \( 2(x + 3) \).

Step1: Analyze the model

There are 4 rows of tiles, and each row has 2 \( x \)-tiles. So each row represents \( x + x \), or \( 2x \).

Step2: Write the multiplication expression

To represent 4 rows of \( 2x \), the multiplication expression is \( 4(2x) \) or \( 8x \) (but in factored form, it's \( 4 \times 2x = 8x \), but the expression representing the model as a multiplication of rows and the expression per row is \( 4(2x) \)). Wait, actually, looking at the tiles: there are 4 rows, each with 2 \( x \)-tiles. So the number of \( x \)-tiles per row is 2, number of rows is 4. So the multiplication expression is \( 4 \times 2x = 8x \), but if we consider the row as \( 2x \), then it's \( 4(2x) \).
Wait, more accurately: each row has 2 \( x \)-tiles, so each row is \( 2x \), and there are 4 rows. So the expression is \( 4 \times 2x = 8x \), but the multiplication expression representing the model (rows times row expression) is \( 4(2x) \).

Step1: Analyze the model

There are 2 groups (rows) of tiles. Each group has \( x^2 + x \) (one \( x^2 \)-tile and one \( x \)-tile).

Step2: Write the multiplication expression

To represent 2 groups of \( x^2 + x \), the multiplication expression is \( 2(x^2 + x) \).

Answer:

\( 2(x + 3) \)

Problem 15