(3a^2+1)-(4+2a^2) Standard Form

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions in Standard Form

In algebra, simplifying expressions involves combining like terms to express the expression in a more concise and readable form. This is particularly important when dealing with polynomials, which are expressions containing variables raised to non-negative integer powers.

Let's look at the expression (3a^2 + 1) - (4 + 2a^2) and simplify it to its standard form.

Understanding the Process

1. Distribute the negative sign: Remember that subtracting a term is the same as adding its negative. So, we can rewrite the expression as: 3a^2 + 1 - 4 - 2a^2

2. Combine like terms: Identify the terms with the same variable and exponent. Here, we have two terms with a^2 and two constant terms: (3a^2 - 2a^2) + (1 - 4)

3. Simplify: Perform the arithmetic operations on the coefficients: a^2 - 3

Standard Form

The standard form of a polynomial is written in descending order of exponents. In this case, our simplified expression, a^2 - 3, is already in standard form.

Conclusion

By understanding the steps of distributing the negative sign and combining like terms, we can easily simplify expressions like (3a^2 + 1) - (4 + 2a^2) to their standard form, a^2 - 3. This process is fundamental in algebra and allows us to work efficiently with polynomial expressions.