(3a-4b+2c)(a+2b-5c)

2 min read Jun 16, 2024
(3a-4b+2c)(a+2b-5c)

Expanding the Expression: (3a - 4b + 2c)(a + 2b - 5c)

This article will guide you through expanding the expression (3a - 4b + 2c)(a + 2b - 5c) using the distributive property.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend of the sum by the number and then adding the products. In simpler terms, it allows us to "distribute" the multiplication over each term inside the parentheses.

Applying the Distributive Property

  1. Multiply the first term of the first expression (3a) by each term in the second expression:

    • 3a * a = 3a²
    • 3a * 2b = 6ab
    • 3a * -5c = -15ac
  2. Multiply the second term of the first expression (-4b) by each term in the second expression:

    • -4b * a = -4ab
    • -4b * 2b = -8b²
    • -4b * -5c = 20bc
  3. Multiply the third term of the first expression (2c) by each term in the second expression:

    • 2c * a = 2ac
    • 2c * 2b = 4bc
    • 2c * -5c = -10c²
  4. Add all the products together:

    • 3a² + 6ab - 15ac - 4ab - 8b² + 20bc + 2ac + 4bc - 10c²
  5. Combine like terms:

    • 3a² - 8b² - 10c² + 2ab - 13ac + 24bc

Final Result

The expanded form of (3a - 4b + 2c)(a + 2b - 5c) is 3a² - 8b² - 10c² + 2ab - 13ac + 24bc.

Conclusion

By applying the distributive property, we successfully expanded the given expression. Remember, it's crucial to carefully distribute each term and then combine like terms for a simplified result.

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