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

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