%E2%88%92(4%2B2a2)-in-standard-form.jpeg "(3a2+1)−(4+2a2) In Standard Form")
Simplifying Algebraic Expressions: (3a² + 1) - (4 + 2a²)
This article will guide you through the process of simplifying the algebraic expression (3a² + 1) - (4 + 2a²) and writing it in standard form.
Understanding the Problem
The expression (3a² + 1) - (4 + 2a²) involves combining terms with the same variable and exponent. To simplify this expression, we need to distribute the negative sign and then combine like terms.
Steps to Simplify
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Distribute the negative sign: Remember that subtracting a quantity is the same as adding its negative. This means we can rewrite the expression as: (3a² + 1) + (-1)(4 + 2a²)
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Multiply through the parentheses: 3a² + 1 - 4 - 2a²
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Combine like terms: Group the terms with the same variable and exponent: (3a² - 2a²) + (1 - 4)
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Simplify: a² - 3
Standard Form
The expression a² - 3 is now in standard form. This means the terms are arranged in descending order of their exponents, starting with the highest power of the variable.
Conclusion
By following the steps above, we have successfully simplified the expression (3a² + 1) - (4 + 2a²) and written it in standard form as a² - 3. This process involves distributing the negative sign, combining like terms, and arranging the terms in descending order of their exponents.