(x%2B1)-in-standard-form.jpeg "(2x+5)(x+1) In Standard Form")
Expanding and Simplifying (2x + 5)(x + 1)
This article will guide you through the process of expanding and simplifying the expression (2x + 5)(x + 1) into standard form.
Understanding Standard Form
A polynomial expression is in standard form when its terms are arranged in descending order of their exponents. For example, a quadratic expression in standard form would be ax² + bx + c, where a, b, and c are constants.
Expanding the Expression
To expand the expression (2x + 5)(x + 1), we use the distributive property. This involves multiplying each term in the first set of parentheses by each term in the second set of parentheses.
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Multiply 2x by each term in (x + 1):
- 2x * x = 2x²
- 2x * 1 = 2x
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Multiply 5 by each term in (x + 1):
- 5 * x = 5x
- 5 * 1 = 5
Combining Like Terms
Now, we have the expanded expression: 2x² + 2x + 5x + 5. To simplify it to standard form, we combine the like terms:
- 2x² remains as it is
- 2x + 5x = 7x
- 5 remains as it is
Final Result
Therefore, the expression (2x + 5)(x + 1) in standard form is: 2x² + 7x + 5