(6n%2B1)-multiplying-polynomials.jpeg "(2n+2)(6n+1) Multiplying Polynomials")
Multiplying Polynomials: (2n+2)(6n+1)
In this article, we will explore how to multiply the polynomials (2n+2) and (6n+1). This is a common operation in algebra, and understanding the process is crucial for solving various equations and expressions.
The Distributive Property
The key to multiplying polynomials is the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number.
For example:
- a(b + c) = ab + ac
Applying the Distributive Property
Let's apply the distributive property to multiply (2n+2)(6n+1):
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Distribute the first term of the first polynomial: (2n + 2)(6n + 1) = 2n(6n + 1) + 2(6n + 1)
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Distribute the second term of the first polynomial: 2n(6n + 1) + 2(6n + 1) = 12n² + 2n + 12n + 2
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Combine like terms: 12n² + 2n + 12n + 2 = 12n² + 14n + 2
Therefore, the product of (2n+2) and (6n+1) is 12n² + 14n + 2.
Conclusion
Multiplying polynomials like (2n+2) and (6n+1) involves applying the distributive property. By distributing each term of the first polynomial to the terms of the second polynomial, we can obtain the expanded form of the product, which is 12n² + 14n + 2 in this case. This process is essential for simplifying expressions and solving various algebraic problems.