(5n+2)^2

Jasonbradley

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Jun 16, 2024

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Expanding (5n + 2)^2

The expression (5n + 2)^2 represents the square of a binomial. To expand it, we can use the FOIL method (First, Outer, Inner, Last) or the square of a binomial pattern.

Using the FOIL Method:

1. First: Multiply the first terms of each binomial: (5n) * (5n) = 25n^2
2. Outer: Multiply the outer terms: (5n) * (2) = 10n
3. Inner: Multiply the inner terms: (2) * (5n) = 10n
4. Last: Multiply the last terms: (2) * (2) = 4

Now, combine the terms: 25n^2 + 10n + 10n + 4

Finally, simplify by combining the middle terms: 25n^2 + 20n + 4

Using the Square of a Binomial Pattern:

The square of a binomial pattern states: (a + b)^2 = a^2 + 2ab + b^2

In our case, a = 5n and b = 2. Applying the pattern:

(5n + 2)^2 = (5n)^2 + 2(5n)(2) + 2^2

Simplifying: 25n^2 + 20n + 4

Conclusion

Both methods result in the same expanded expression: 25n^2 + 20n + 4.

This expression represents a quadratic trinomial with a leading coefficient of 25, a linear coefficient of 20, and a constant term of 4. It can be used in various algebraic manipulations and problem-solving scenarios.