(2x%5E3%2B4x%5E2-5)-standard-form.jpeg "(3x-1)(2x^3+4x^2-5) Standard Form")
Expanding and Simplifying (3x-1)(2x^3+4x^2-5)
To express the product of (3x-1)(2x^3+4x^2-5) in standard form, we need to expand the expression and combine like terms.
Expanding the Expression
We can use the distributive property (also known as FOIL) to multiply the two expressions:
(3x - 1)(2x^3 + 4x^2 - 5)
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Multiply 3x by each term in the second expression:
- 3x * 2x^3 = 6x^4
- 3x * 4x^2 = 12x^3
- 3x * -5 = -15x
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Multiply -1 by each term in the second expression:
- -1 * 2x^3 = -2x^3
- -1 * 4x^2 = -4x^2
- -1 * -5 = 5
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Combine all the terms: 6x^4 + 12x^3 - 15x - 2x^3 - 4x^2 + 5
Simplifying the Expression
Now, we combine the like terms:
6x^4 + (12x^3 - 2x^3) - 4x^2 - 15x + 5
This simplifies to:
6x^4 + 10x^3 - 4x^2 - 15x + 5
Standard Form
The standard form of a polynomial is when the terms are arranged in descending order of their exponents. Our expression is already in standard form:
6x^4 + 10x^3 - 4x^2 - 15x + 5
Therefore, the expanded and simplified form of (3x-1)(2x^3+4x^2-5) in standard form is 6x^4 + 10x^3 - 4x^2 - 15x + 5.