(3x%5E2-2x%2B5).jpeg "(2x+3)(3x^2-2x+5)")
Expanding the Expression (2x + 3)(3x² - 2x + 5)
This article will guide you through the process of expanding the given expression (2x + 3)(3x² - 2x + 5).
Understanding the Problem
We have a product of two expressions:
- (2x + 3): A binomial, containing two terms
- (3x² - 2x + 5): A trinomial, containing three terms
To expand this expression, we need to multiply each term in the first expression by each term in the second expression.
Applying the Distributive Property
The distributive property states that: a(b + c) = ab + ac. We can use this principle to expand our expression.
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Multiply (2x) by each term in the trinomial:
- (2x)(3x²) = 6x³
- (2x)(-2x) = -4x²
- (2x)(5) = 10x
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Multiply (3) by each term in the trinomial:
- (3)(3x²) = 9x²
- (3)(-2x) = -6x
- (3)(5) = 15
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Combine all the terms:
- 6x³ - 4x² + 10x + 9x² - 6x + 15
Simplifying the Expression
Finally, we combine like terms to get our simplified expression:
6x³ + 5x² + 4x + 15
Therefore, the expanded form of (2x + 3)(3x² - 2x + 5) is 6x³ + 5x² + 4x + 15.