(2x+6)^2 Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying (2x + 6)^2

The expression (2x + 6)^2 represents the square of the binomial (2x + 6). To simplify this expression, we can utilize the FOIL method or the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us expand the product of two binomials:

1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x^2
2. Outer: Multiply the outer terms of the binomials: (2x) * (6) = 12x
3. Inner: Multiply the inner terms of the binomials: (6) * (2x) = 12x
4. Last: Multiply the last terms of the binomials: (6) * (6) = 36

Now, combine all the terms: 4x^2 + 12x + 12x + 36

Finally, simplify by combining like terms: 4x^2 + 24x + 36

Using the Square of a Binomial Formula

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

Applying this formula to our expression:

• a = 2x
• b = 6

Therefore, (2x + 6)^2 = (2x)^2 + 2(2x)(6) + 6^2

Simplifying: 4x^2 + 24x + 36

Conclusion

Both methods result in the same simplified expression: 4x^2 + 24x + 36. You can choose whichever method you find easier or more efficient.