(2n%2B6)-box-method.jpeg "(4n+1)(2n+6) Box Method")
The Box Method for Multiplying (4n + 1)(2n + 6)
The box method is a visual and systematic way to multiply binomials, making it easier to understand and avoid errors. Here's how it works for multiplying (4n + 1)(2n + 6):
Setting up the Box
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Draw a 2x2 box: This represents the two terms in each binomial.
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Label the rows and columns: The top row represents the terms of (4n + 1) and the left column represents the terms of (2n + 6).
4n 1 2n 6
Filling the Box
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Multiply each row and column: Multiply the terms that correspond to the intersection of each row and column.
4n 1 2n 8n² 2n 6 24n 6
Combining the Terms
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Identify all the terms in the box: You have four terms: 8n², 2n, 24n, and 6.
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Combine like terms: Combine the terms with the same variable and exponent.
- 8n² + 2n + 24n + 6
- 8n² + 26n + 6
Therefore, (4n + 1)(2n + 6) = 8n² + 26n + 6.
Benefits of the Box Method
- Visual Representation: The box method helps to visualize the multiplication process, making it easier to understand.
- Organization: The box provides a structured way to organize all the terms, minimizing the chance of missing any.
- Error Reduction: It makes it less likely to make mistakes with signs or coefficients.
The box method is a powerful tool for multiplying binomials and can be applied to any similar problem.