Simplifying Expressions
Simplifying expressions is a process of reducing a mathematical expression to its simplest form. There are several different techniques that can be used to simplify expressions, but the most common methods involve combining like terms and using the order of operations.
Step 1: Understand the order of operations The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is often abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Step 2: Simplify expressions inside parentheses Start by simplifying any expressions inside parentheses first. If there are multiple sets of parentheses, work on the innermost set first and then work your way outwards.
Step 3: Apply exponents Next, simplify any expressions with exponents by raising the base to the power indicated by the exponent.
Step 4: Perform multiplication and division Next, perform any multiplication or division from left to right.
Step 5: Perform addition and subtraction Finally, perform any addition or subtraction from left to right.
Step 6: Combining like terms Combining like terms is the process of adding or subtracting any terms that have the same variable and exponent. Like terms can be combined by adding or subtracting their coefficients.
Examples:
- 2x + 3x = (2+3)x = 5x
- 2x^2 + 3x^2 = (2+3)x^2 = 5x^2
- 3y + 2y + 4y = (3+2+4)y = 9y
Note: After simplifying, if the expression still contain fraction or irrational numbers, we may factorize them further.
In conclusion, simplifying expressions involves understanding the order of operations, simplifying expressions inside parentheses, applying exponents, performing multiplication and division, performing addition and subtraction, and combining like terms. By following these steps, you can simplify any mathematical expression.
