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(m+2)(8+3m)-2(1-m)(m-7)

2 min read Jun 16, 2024
(m+2)(8+3m)-2(1-m)(m-7)

Expanding and Simplifying the Expression (m+2)(8+3m)-2(1-m)(m-7)

This article will guide you through the process of expanding and simplifying the expression (m+2)(8+3m)-2(1-m)(m-7).

Expanding the Expressions

First, we need to expand the products using the distributive property (also known as FOIL method).

  • (m+2)(8+3m):
    • Multiply each term in the first parenthesis by each term in the second parenthesis.
    • m * 8 + m * 3m + 2 * 8 + 2 * 3m
    • 8m + 3m² + 16 + 6m
  • (1-m)(m-7):
    • 1 * m + 1 * (-7) + (-m) * m + (-m) * (-7)
    • m - 7 - m² + 7m

Now we have: (8m + 3m² + 16 + 6m) - 2 (m - 7 - m² + 7m)

Simplifying the Expression

Let's continue by distributing the -2:

  • (8m + 3m² + 16 + 6m) - 2m + 14 + 2m² - 14m

Finally, combine like terms:

  • (3m² + 2m²) + (8m + 6m - 2m - 14m) + (16 + 14)

This gives us:

  • 5m² - 2m + 30

Conclusion

The simplified form of the expression (m+2)(8+3m)-2(1-m)(m-7) is 5m² - 2m + 30.

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