(2x+6)(2x+8) Trinomial

Jasonbradley

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Jun 16, 2024

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Expanding the Trinomial (2x + 6)(2x + 8)

This article will guide you through expanding the trinomial (2x + 6)(2x + 8).

Understanding Trinomials

A trinomial is a polynomial with three terms. To expand this expression, we can use the FOIL method:

• First: Multiply the first terms of each binomial.
• Outer: Multiply the outer terms of each binomial.
• Inner: Multiply the inner terms of each binomial.
• Last: Multiply the last terms of each binomial.

Expanding the Expression

Let's apply the FOIL method to (2x + 6)(2x + 8):

1. First: (2x) * (2x) = 4x²
2. Outer: (2x) * (8) = 16x
3. Inner: (6) * (2x) = 12x
4. Last: (6) * (8) = 48

Now, we combine the terms:

4x² + 16x + 12x + 48

Finally, we simplify by combining the like terms:

4x² + 28x + 48

Conclusion

Therefore, the expanded form of the trinomial (2x + 6)(2x + 8) is 4x² + 28x + 48. The FOIL method provides a systematic way to expand binomials and is a valuable tool in algebra.