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Expanding the Expression (2x-3)(2x^2-5x-8)
This article will explore the expansion of the expression (2x-3)(2x^2-5x-8) using the distributive property.
Understanding the Distributive Property
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
This property allows us to multiply a sum by a number by multiplying each term of the sum individually.
Expanding the Expression
To expand (2x-3)(2x^2-5x-8), we'll apply the distributive property twice.
Step 1: Distribute (2x-3) over the first term of the second expression (2x^2).
(2x - 3)(2x^2 - 5x - 8) = 2x(2x^2 - 5x - 8) - 3(2x^2 - 5x - 8)
Step 2: Distribute 2x and -3 over the remaining terms.
= 4x^3 - 10x^2 - 16x - 6x^2 + 15x + 24
Step 3: Combine like terms.
= 4x^3 - 16x^2 - x + 24
The Expanded Form
Therefore, the expanded form of (2x-3)(2x^2-5x-8) is 4x^3 - 16x^2 - x + 24.
Conclusion
Expanding expressions like this using the distributive property is a fundamental skill in algebra. It allows us to simplify expressions and perform various algebraic operations. By understanding the distributive property and applying it carefully, we can easily expand complex expressions like the one presented above.