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.Select The Correct Answer From Each Drop-down Menu.
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Introduction
Algebra tiles are a visual representation of algebraic expressions, making it easier to understand and manipulate them. In this problem, we will use algebra tiles to model the product of (z+2)(z-3). We will then remove the zero pairs and rewrite the product in simplest form.
Step 1: Create the Algebra Tile Grid
To create the algebra tile grid, we need to represent the variables z and the constants 2 and 3 using algebra tiles. We will use the following tiles:
- Variable tiles: Represented by a square tile with a variable z written on it.
- Constant tiles: Represented by a square tile with a constant value written on it.
- Zero pairs: Represented by two square tiles with a zero written on each.
We will start by creating the algebra tile grid for the expression (z+2)(z-3).
Algebra Tile Grid for (z+2)(z-3)
| z | 2 | -3 | |
|---|---|---|---|
| z | |||
| 2 | |||
| -3 |
Step 2: Multiply the Expressions
To multiply the expressions (z+2) and (z-3), we need to multiply each term in the first expression by each term in the second expression.
Multiplying (z+2) and (z-3)
(z+2)(z-3) = z(z-3) + 2(z-3)
Step 3: Distribute and Simplify
To distribute and simplify the expression, we need to multiply each term in the first expression by each term in the second expression and then combine like terms.
Distributing and Simplifying
z(z-3) = z^2 - 3z 2(z-3) = 2z - 6
Now, we can combine like terms:
z^2 - 3z + 2z - 6
Step 4: Combine Like Terms
To combine like terms, we need to add or subtract the coefficients of the same variables.
Combining Like Terms
z^2 - 3z + 2z - 6 = z^2 - z - 6
Step 5: Remove Zero Pairs
To remove zero pairs, we need to identify the zero pairs in the algebra tile grid and remove them.
Removing Zero Pairs
| z | 2 | -3 | |
|---|---|---|---|
| z | |||
| 2 | |||
| -3 |
There are no zero pairs in this algebra tile grid.
Step 6: Rewrite the Product in Simplest Form
To rewrite the product in simplest form, we need to simplify the expression by combining like terms.
Rewriting the Product in Simplest Form
z^2 - z - 6
This is the simplest form of the product.
Conclusion
In this problem, we used algebra tiles to model the product of (z+2)(z-3). We then removed the zero pairs and rewrote the product in simplest form. The final answer is z^2 - z - 6.
Final Answer
- Variable term: z^2
- Coefficient of z: -1
- Constant term: -6
The final answer is:
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Frequently Asked Questions
Q: What are algebra tiles?
A: Algebra tiles are a visual representation of algebraic expressions, making it easier to understand and manipulate them.
Q: What types of tiles are used in algebra tiles?
A: The following types of tiles are used in algebra tiles:
- Variable tiles: Represented by a square tile with a variable written on it.
- Constant tiles: Represented by a square tile with a constant value written on it.
- Zero pairs: Represented by two square tiles with a zero written on each.
Q: How do I create an algebra tile grid?
A: To create an algebra tile grid, you need to represent the variables and constants using algebra tiles. You can start by creating a grid with the variables and constants on the top row and the corresponding tiles on the bottom row.
Q: How do I multiply expressions using algebra tiles?
A: To multiply expressions using algebra tiles, you need to multiply each term in the first expression by each term in the second expression. You can then combine like terms and simplify the expression.
Q: How do I remove zero pairs from an algebra tile grid?
A: To remove zero pairs from an algebra tile grid, you need to identify the zero pairs and remove them. Zero pairs are represented by two square tiles with a zero written on each.
Q: How do I rewrite a product in simplest form using algebra tiles?
A: To rewrite a product in simplest form using algebra tiles, you need to simplify the expression by combining like terms. You can then remove any zero pairs and rewrite the product in simplest form.
Q: What is the final answer for the product of (z+2)(z-3)?
A: The final answer for the product of (z+2)(z-3) is z^2 - z - 6.
Q: How do I determine the coefficient of a variable in an algebra tile grid?
A: To determine the coefficient of a variable in an algebra tile grid, you need to count the number of tiles representing the variable. The coefficient is then determined by the number of tiles.
Q: How do I determine the constant term in an algebra tile grid?
A: To determine the constant term in an algebra tile grid, you need to count the number of constant tiles. The constant term is then determined by the number of tiles.
Q: What are some common mistakes to avoid when using algebra tiles?
A: Some common mistakes to avoid when using algebra tiles include:
- Not removing zero pairs: Failing to remove zero pairs can lead to incorrect answers.
- Not combining like terms: Failing to combine like terms can lead to incorrect answers.
- Not simplifying the expression: Failing to simplify the expression can lead to incorrect answers.
Tips and Tricks
Tip 1: Use a systematic approach
When using algebra tiles, it's essential to use a systematic approach to ensure accuracy. Start by creating the algebra tile grid, then multiply the expressions, combine like terms, and simplify the expression.
Tip 2: Check for zero pairs
When using algebra tiles, it's essential to check for zero pairs and remove them. Zero pairs can lead to incorrect answers if not removed.
Tip 3: Simplify the expression
When using algebra tiles, it's essential to simplify the expression by combining like terms. Simplifying the expression can help ensure accuracy and avoid incorrect answers.
Conclusion
Algebra tiles are a powerful tool for understanding and manipulating algebraic expressions. By following the steps outlined in this article, you can use algebra tiles to model the product of (z+2)(z-3) and rewrite the product in simplest form. Remember to use a systematic approach, check for zero pairs, and simplify the expression to ensure accuracy.
Final Answer
- Variable term: z^2
- Coefficient of z: -1
- Constant term: -6
The final answer is: