Question
Use the algebra tiles to write the product of (2 - 2x) (3 - 5x)
Answers
GPT-4o mini
To find the product of \( (2 - 2x)(3 - 5x) \) using algebra tiles, you can follow these steps:
1. **Identify the terms**: The expression consists of two binomials:
- The first binomial is \( 2 - 2x \).
- The second binomial is \( 3 - 5x \).
2. **Set up the area model**: We can represent this product using an area model or algebra tiles, where one binomial is represented along one side of the rectangle and the other along another side.
3. **Draw the rectangle**: Create a rectangle divided into areas based on the terms of each binomial:
- The width of the rectangle would be \( 2 \) (from \( 2 - 2x \)) and \( -2x \).
- The height of the rectangle would be \( 3 \) and \( -5x \).
4. **Multiply the terms**: You now fill in the areas of each section of your rectangle by multiplying the sides:
- The area for the \( 2 \times 3 \) section is \( 6 \).
- The area for the \( 2 \times (-5x) \) section is \( -10x \).
- The area for the \( -2x \times 3 \) section is \( -6x \).
- The area for the \( -2x \times (-5x) \) section is \( 10x^2 \).
5. **Combine the areas**: Now add together the results from each section:
- Combine like terms:
- The constant term is \( 6 \).
- The \( x \) terms are \( -10x - 6x = -16x \).
- The \( x^2 \) term is \( 10x^2 \).
So, when you combine all the terms, the final product of \( (2 - 2x)(3 - 5x) \) is:
\[
10x^2 - 16x + 6
\]
This represents the product of the two binomials.
1. **Identify the terms**: The expression consists of two binomials:
- The first binomial is \( 2 - 2x \).
- The second binomial is \( 3 - 5x \).
2. **Set up the area model**: We can represent this product using an area model or algebra tiles, where one binomial is represented along one side of the rectangle and the other along another side.
3. **Draw the rectangle**: Create a rectangle divided into areas based on the terms of each binomial:
- The width of the rectangle would be \( 2 \) (from \( 2 - 2x \)) and \( -2x \).
- The height of the rectangle would be \( 3 \) and \( -5x \).
4. **Multiply the terms**: You now fill in the areas of each section of your rectangle by multiplying the sides:
- The area for the \( 2 \times 3 \) section is \( 6 \).
- The area for the \( 2 \times (-5x) \) section is \( -10x \).
- The area for the \( -2x \times 3 \) section is \( -6x \).
- The area for the \( -2x \times (-5x) \) section is \( 10x^2 \).
5. **Combine the areas**: Now add together the results from each section:
- Combine like terms:
- The constant term is \( 6 \).
- The \( x \) terms are \( -10x - 6x = -16x \).
- The \( x^2 \) term is \( 10x^2 \).
So, when you combine all the terms, the final product of \( (2 - 2x)(3 - 5x) \) is:
\[
10x^2 - 16x + 6
\]
This represents the product of the two binomials.