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

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)

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)

Simplify the resulting terms:
(4−b)(5b^2+5b−4) = 20b^2 + 20b  16  5b^3  5b^2 + 4b

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.