What is this Expression in Simplest Form? – A Comprehensive Guide

What does it mean to simplify an expression?

Simplifying an expression means to reduce it to its most basic form. This is done by combining like terms, removing unnecessary parentheses, and reducing fractions to their lowest terms. The simplest form of an expression is the one that cannot be simplified any further.

Steps to simplify an expression in the simplest form

1. Combine like terms: Look for terms that have the same variable and exponent and combine them.
2. Remove parentheses: Use the distributive property to remove parentheses.
3. Reduce fractions: Divide the numerator and denominator by their greatest common factor to reduce fractions to their lowest terms.
4. Check for any remaining like terms: Repeat step 1 until there are no more like terms to combine.
5. Check for any remaining parentheses: Repeat step 2 until there are no more parentheses to remove.
6. Check for any remaining fractions: Repeat step 3 until there are no more fractions to reduce.

Examples of simplifying expressions in the simplest form

Example 1: Simplify 3x + 2x – 5

1. Combine like terms: 3x + 2x = 5x
2. Check for any remaining like terms: None
3. The simplest form of the expression is 5x – 5.

Example 2: Simplify 2(3x + 4) – 5(2x – 3)

1. Remove parentheses: 2(3x) + 2(4) – 5(2x) + 5(3) = 6x + 8 – 10x + 15
2. Combine like terms: 6x – 10x = -4x, 8 + 15 = 23
3. Check for any remaining like terms: None
4. The simplest form of the expression is -4x + 23.

Example 3: Simplify (2x^2 + 4x) / 2

1. Reduce fractions: (2x^2 / 2) + (4x / 2) = x^2 + 2x
2. Check for any remaining fractions: None
3. Check for any remaining like terms: None
4. The simplest form of the expression is x^2 + 2x.

Conclusion

Simplifying an expression in the simplest form is an important skill in algebra. By following the steps outlined in this guide, you can simplify any expression to its most basic form. Remember to always check for like terms, parentheses, and fractions, and to reduce them as much as possible. With practice, you will become proficient in simplifying expressions and be able to tackle more complex problems.