Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To solve the binomial multiplication [tex]\((2x - 3)(x + 7)\)[/tex] and determine the value of the letters in the given table, let's break down the multiplication step-by-step.
1. Multiplying each term in [tex]\(2x - 3\)[/tex] by each term in [tex]\(x + 7\)[/tex]:
[tex]\[ (2x - 3)(x + 7) \][/tex]
This can be expanded as:
[tex]\[ = (2x) \cdot (x) + (2x) \cdot (7) + (-3) \cdot (x) + (-3) \cdot (7) \][/tex]
2. Calculate each part of the expansion:
[tex]\[ = 2x^2 \quad \text{(from } 2x \cdot x\text{)} \][/tex]
[tex]\[ = 14x \quad \text{(from } 2x \cdot 7\text{, which is B in the table)} \][/tex]
[tex]\[ = -3x \quad \text{(from } -3 \cdot x\text{, which is A in the table)} \][/tex]
[tex]\[ = -21 \quad \text{(from } -3 \cdot 7\text{, which is C in the table)} \][/tex]
Now we collect the terms from the table:
- [tex]$A = -3x$[/tex]
- [tex]$B = 14x$[/tex]
- [tex]$C = -21$[/tex]
To find which letters represent like terms, we look for terms with the same variable part.
- [tex]\(A = -3x\)[/tex] (contains [tex]\(x\)[/tex])
- [tex]\(B = 14x\)[/tex] (contains [tex]\(x\)[/tex])
- [tex]\(C = -21\)[/tex] (constant term with no [tex]\(x\)[/tex])
So, the like terms are [tex]$A$[/tex] and [tex]$B$[/tex] because they both contain the variable [tex]\(x\)[/tex].
### Summary:
- [tex]\(A = -3x\)[/tex]
- [tex]\(B = 14x\)[/tex]
- [tex]\(C = -21\)[/tex]
- The letters representing like terms are [tex]\(A\)[/tex] and [tex]\(B\)[/tex]
1. Multiplying each term in [tex]\(2x - 3\)[/tex] by each term in [tex]\(x + 7\)[/tex]:
[tex]\[ (2x - 3)(x + 7) \][/tex]
This can be expanded as:
[tex]\[ = (2x) \cdot (x) + (2x) \cdot (7) + (-3) \cdot (x) + (-3) \cdot (7) \][/tex]
2. Calculate each part of the expansion:
[tex]\[ = 2x^2 \quad \text{(from } 2x \cdot x\text{)} \][/tex]
[tex]\[ = 14x \quad \text{(from } 2x \cdot 7\text{, which is B in the table)} \][/tex]
[tex]\[ = -3x \quad \text{(from } -3 \cdot x\text{, which is A in the table)} \][/tex]
[tex]\[ = -21 \quad \text{(from } -3 \cdot 7\text{, which is C in the table)} \][/tex]
Now we collect the terms from the table:
- [tex]$A = -3x$[/tex]
- [tex]$B = 14x$[/tex]
- [tex]$C = -21$[/tex]
To find which letters represent like terms, we look for terms with the same variable part.
- [tex]\(A = -3x\)[/tex] (contains [tex]\(x\)[/tex])
- [tex]\(B = 14x\)[/tex] (contains [tex]\(x\)[/tex])
- [tex]\(C = -21\)[/tex] (constant term with no [tex]\(x\)[/tex])
So, the like terms are [tex]$A$[/tex] and [tex]$B$[/tex] because they both contain the variable [tex]\(x\)[/tex].
### Summary:
- [tex]\(A = -3x\)[/tex]
- [tex]\(B = 14x\)[/tex]
- [tex]\(C = -21\)[/tex]
- The letters representing like terms are [tex]\(A\)[/tex] and [tex]\(B\)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.