(x%2B5)(2x-1)-in-standard-form.jpeg "(x-5)(x+5)(2x-1) In Standard Form")
Expanding (x-5)(x+5)(2x-1) into Standard Form
This article will guide you through the process of expanding the expression (x-5)(x+5)(2x-1) and putting it into standard form.
Understanding Standard Form
Standard form for a polynomial refers to arranging the terms in descending order of their exponents. For example, a quadratic polynomial in standard form would be ax² + bx + c, where a, b, and c are constants.
Expanding the Expression
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Focus on the first two factors: Start by expanding (x-5)(x+5). This is a difference of squares pattern, where (a-b)(a+b) = a² - b². Applying this pattern, we get:
(x-5)(x+5) = x² - 5² = x² - 25
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Multiply the result by the remaining factor: Now, we have (x² - 25)(2x-1). We need to distribute each term from the first factor to each term in the second factor.
(x² - 25)(2x-1) = x² * (2x-1) - 25 * (2x-1) = 2x³ - x² - 50x + 25
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Simplify and Rearrange: Finally, combine like terms and arrange them in descending order of exponents:
2x³ - x² - 50x + 25
Conclusion
Therefore, the expression (x-5)(x+5)(2x-1) in standard form is 2x³ - x² - 50x + 25. By understanding the difference of squares pattern and following the steps of distribution and simplification, we successfully transformed the original expression into its standard form.