(4−b)(5b2+5b−4)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (4−b)(5b^2+5b−4)

This article will guide you through the process of expanding the expression (4−b)(5b^2+5b−4).

Understanding the Concept

Expanding an expression means multiplying out the terms within parentheses. This can be achieved using the distributive property of multiplication over addition. In simpler terms, we multiply each term in the first set of parentheses by each term in the second set of parentheses.

Expanding the Expression

1. Multiply the first term of the first set of parentheses by each term of the second set:

   (4−b)(5b^2+5b−4) = 4(5b^2) + 4(5b) + 4(-4)

2. Multiply the second term of the first set of parentheses by each term of the second set:

   (4−b)(5b^2+5b−4) = -b(5b^2) - b(5b) - b(-4)

3. Simplify the resulting terms:

   (4−b)(5b^2+5b−4) = 20b^2 + 20b - 16 - 5b^3 - 5b^2 + 4b

4. Combine like terms:

   (4−b)(5b^2+5b−4) = -5b^3 + 15b^2 + 24b - 16

Conclusion

The expanded form of the expression (4−b)(5b^2+5b−4) is -5b^3 + 15b^2 + 24b - 16. This process demonstrates the importance of using the distributive property to accurately expand algebraic expressions.