(3x%5E2-2x-5).jpeg "(2x+1)(3x^2-2x-5)")
Expanding the Expression: (2x+1)(3x^2-2x-5)
This article will explore the expansion of the expression (2x+1)(3x^2-2x-5). This type of expression involves multiplying two binomials, and the process of expanding it involves applying 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 in the sum by that number and then adding the products. In this case, we'll be applying the distributive property twice.
Expanding the Expression
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First, we distribute the '2x' from the first binomial across the terms in the second binomial:
(2x)(3x^2) + (2x)(-2x) + (2x)(-5)
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Next, we distribute the '1' from the first binomial across the terms in the second binomial:
(1)(3x^2) + (1)(-2x) + (1)(-5)
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Now we simplify the expression by performing the multiplications:
6x^3 - 4x^2 - 10x + 3x^2 - 2x - 5
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Finally, we combine like terms:
6x^3 - x^2 - 12x - 5
Therefore, the expanded form of (2x+1)(3x^2-2x-5) is 6x^3 - x^2 - 12x - 5.
Conclusion
Expanding expressions like (2x+1)(3x^2-2x-5) is a fundamental skill in algebra. By understanding the distributive property and applying it systematically, we can simplify such expressions and obtain their expanded form. This skill is crucial for various algebraic operations and problem-solving techniques.