(6n%2B1)-answer.jpeg "(2n+2)(6n+1) Answer")
Expanding the Expression (2n+2)(6n+1)
This article will guide you through expanding the expression (2n+2)(6n+1) using the distributive property, often referred to as FOIL (First, Outer, Inner, Last).
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend of the sum by the number and then adding the products.
In our case, we have two binomials, (2n+2) and (6n+1). We need to distribute each term of the first binomial to both terms of the second binomial.
Expanding Using FOIL
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First: Multiply the first terms of each binomial: (2n) * (6n) = 12n²
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Outer: Multiply the outer terms of the binomials: (2n) * (1) = 2n
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Inner: Multiply the inner terms of the binomials: (2) * (6n) = 12n
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Last: Multiply the last terms of each binomial: (2) * (1) = 2
Combining the Terms
Now, we add all the terms we obtained:
12n² + 2n + 12n + 2
Finally, we combine the like terms:
12n² + 14n + 2
Conclusion
Therefore, the expanded form of (2n+2)(6n+1) is 12n² + 14n + 2. This process can be applied to any pair of binomials, allowing you to simplify expressions and solve algebraic problems.