Question

Complete the algebra tile grid to model the product of (z + 2)(z- 3).

Remove the zero pairs. Then rewrite the product in simplest form.

Answer 1

Explanation:

To model the product of (z + 2)(z - 3) using an algebra tile grid, we can represent each term as a set of tiles and arrange them accordingly. Here's how you can complete the grid:

First, let's represent z + 2 using tiles:

1 positive z tile (z) and 1 positive 2 tile (2).

Copy code

| z | 2 |

Next, let's represent z - 3 using tiles:

1 positive z tile (z) and 1 negative 3 tile (-3).

yaml

Copy code

| z | 2 |

| z | -3 |

Now, we need to multiply the corresponding tiles. Each tile in the first set will be multiplied by each tile in the second set. We can create a grid to represent this multiplication:

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |

Finally, we can combine like terms in the grid to simplify the product:

Add the two z^2 tiles together to get z^2.

Add the two 2z tiles together to get 2z.

Add the two -3z tiles together to get -6z.

Combine the -6 and 0 to get -6.

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |

So, the completed algebra tile grid representing the product of (z + 2)(z - 3) is:

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |

To model the product of (z + 2)(z - 3) using an algebra tile grid, we can represent each term as a set of tiles and arrange them accordingly. Here's how you can complete the grid:

First, let's represent z + 2 using tiles:

1 positive z tile (z) and 1 positive 2 tile (2).

Copy code

| z | 2 |

Next, let's represent z - 3 using tiles:

1 positive z tile (z) and 1 negative 3 tile (-3).

yaml

Copy code

| z | 2 |

| z | -3 |

Now, we need to multiply the corresponding tiles. Each tile in the first set will be multiplied by each tile in the second set. We can create a grid to represent this multiplication:

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |

Finally, we can combine like terms in the grid to simplify the product:

Add the two z^2 tiles together to get z^2.

Add the two 2z tiles together to get 2z.

Add the two -3z tiles together to get -6z.

Combine the -6 and 0 to get -6.

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |

So, the completed algebra tile grid representing the product of (z + 2)(z - 3) is:

Copy code

| z | 2 |

z | z^2 | 2z |

-3 |-3z |-6 |