(3x-5)-express-as-a-trinomial.jpeg "(2x-3)(3x-5) Express As A Trinomial")
Expanding (2x-3)(3x-5) into a Trinomial
This problem involves expanding a product of two binomials, resulting in a trinomial. Here's how to do it:
Using the FOIL method
First: Multiply the first terms of each binomial. (2x) * (3x) = 6x²
Outer: Multiply the outer terms of the binomials. (2x) * (-5) = -10x
Inner: Multiply the inner terms of the binomials. (-3) * (3x) = -9x
Last: Multiply the last terms of each binomial. (-3) * (-5) = 15
Now, add all the results together:
6x² - 10x - 9x + 15
Combine the like terms:
6x² - 19x + 15
Therefore, (2x - 3)(3x - 5) expressed as a trinomial is 6x² - 19x + 15.
Alternative Method: Distributive Property
You can also use the distributive property to achieve the same result:
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Distribute the first term of the first binomial: (2x) * (3x - 5) = 6x² - 10x
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Distribute the second term of the first binomial: (-3) * (3x - 5) = -9x + 15
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Combine the results: 6x² - 10x - 9x + 15 = 6x² - 19x + 15
Both methods lead to the same trinomial. Choose whichever method feels more comfortable for you.