(2x-10)(2x+6) Express As A Trinomial

Jasonbradley

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Jun 16, 2024

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Expressing (2x-10)(2x+6) as a Trinomial

To express the product of the binomials (2x-10)(2x+6) as a trinomial, we can use the FOIL method or the distributive property.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us systematically multiply each term in the first binomial with each term in the second binomial.

1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
2. Outer: Multiply the outer terms of the binomials: (2x) * (6) = 12x
3. Inner: Multiply the inner terms of the binomials: (-10) * (2x) = -20x
4. Last: Multiply the last terms of each binomial: (-10) * (6) = -60

Now, add all the terms together: 4x² + 12x - 20x - 60

Finally, combine the like terms: 4x² - 8x - 60

Using the Distributive Property

The distributive property allows us to multiply each term in the first binomial by each term in the second binomial.

1. Distribute (2x-10) over (2x+6): (2x-10) * (2x) + (2x-10) * (6)
2. Distribute again: (2x * 2x) + (-10 * 2x) + (2x * 6) + (-10 * 6)
3. Simplify: 4x² - 20x + 12x - 60
4. Combine like terms: 4x² - 8x - 60

Therefore, (2x-10)(2x+6) expressed as a trinomial is 4x² - 8x - 60.