Question 1

Which algebra tile represents $x^2$ according to the key provided?

Accepted Answer

The large white square

Question 2

What is the product of $(x + 2)(x + 3)$ when using algebra tiles?

Accepted Answer

$x^2 + 5x + 6$

Question 3

If you multiply $(x + 3)(x + 5)$ using algebra tiles, what is the resulting polynomial?

Accepted Answer

$x^2 + 8x + 15$

Question 4

Which tile would you use to represent $-x$ in an algebra tile model?

Accepted Answer

The long red rectangle

Question 5

What is the expanded form of $(2x - 1)(x + 3)$ using algebra tiles?

Accepted Answer

$2x^2 + 5x - 3$

Question 6

If a student uses algebra tiles to multiply $(x + 2)(x + 3)$ and gets $2x^2 + 7x + 6$, what mistake did they most likely make?

Accepted Answer

They doubled the $x^2$ and $x$ terms.

Question 7

Which of the following represents the correct arrangement of tiles for $(x + 2)(x + 3)$?

Accepted Answer

1 $x^2$ tile, 5 $x$ tiles, 6 unit tiles

Question 8

A student is asked to multiply $(x + 2)(x + 3)$ using algebra tiles. What is the first step they should take?

Accepted Answer

Lay out a row of $x$ and $2$ unit tiles and a column of $x$ and $3$ unit tiles.

Question 9

Which of the following is a common error when multiplying polynomials with algebra tiles?

Accepted Answer

Counting the $x^2$ tiles twice

Question 10

If you multiply $(x + 2)(x + 3)$ and arrange the tiles, how many total tiles will you have (counting all $x^2$, $x$, and unit tiles)?

Accepted Answer

12

Question 11

Which expression matches the area model created by multiplying $(x + 2)(x + 3)$ with algebra tiles?

Accepted Answer

$x^2 + 5x + 6$

Question 12

When multiplying $(x + 3)(x + 5)$, what does the $15$ in the answer $x^2 + 8x + 15$ represent in terms of algebra tiles?

Accepted Answer

The number of unit tiles

Question 13

If you use algebra tiles to model $(2x - 1)(x + 3)$, how many $x^2$ tiles should you use?

Accepted Answer

2

Question 14

Which of the following best describes the purpose of using algebra tiles to multiply polynomials?

Accepted Answer

To visually represent the distributive property

Question 15

A student multiplies $(x + 2)(x + 3)$ and gets $x^2 + 6x + 5$. Which step did they likely do incorrectly?

Accepted Answer

They multiplied the constants and the $x$ terms incorrectly.

Multiplying Polynomials Using Algebra Tiles

Study Guide - Practice Questions