Like Terms

Definition

Like terms are algebraic expressions that have the same variable or combination of variables raised to the same power. They can be combined by adding or subtracting their coefficients, as they represent the same quantity in an expression.

5 Must Know Facts For Your Next Test

1. Like terms can be combined by adding or subtracting their coefficients, as they represent the same quantity in an expression.
2. The process of combining like terms is an essential step in simplifying algebraic expressions.
3. Identifying and combining like terms is crucial for performing operations such as addition, subtraction, and multiplication of polynomials.
4. Recognizing like terms is also important when solving equations and inequalities, as it helps in isolating variables.
5. The ability to identify and combine like terms is a fundamental skill in intermediate algebra that underpins many other concepts.

Review Questions

• How can you identify like terms in an algebraic expression?
  • To identify like terms, you need to look for expressions that have the same variable or combination of variables raised to the same power. For example, $3x^2$ and $-5x^2$ are like terms because they both have the variable $x$ raised to the power of 2. Similarly, $2xy$ and $-4xy$ are also like terms, as they both have the variables $x$ and $y$ raised to the power of 1.
• Explain the process of combining like terms and how it simplifies algebraic expressions.
  • Combining like terms involves adding or subtracting the coefficients of expressions that have the same variable or combination of variables raised to the same power. This process simplifies the expression by reducing the number of terms and combining the coefficients. For instance, if an expression contains $2x^2 + 3x^2 - 5x^2$, these terms can be combined by adding the coefficients, resulting in $0x^2$, which can be further simplified to 0. Combining like terms is a crucial step in simplifying algebraic expressions and preparing them for further operations.
• Analyze the importance of understanding like terms in the context of solving equations and inequalities.
  • Recognizing and combining like terms is essential when solving equations and inequalities. By isolating the variable terms on one side of the equation or inequality, you can more easily solve for the unknown. For example, if an equation has the form $3x + 2x - 5 = 7$, combining the like terms $3x$ and $2x$ into $5x$ simplifies the equation to $5x - 5 = 7$, making it easier to solve for $x$. Similarly, in an inequality such as $4y - 2y + 1 geq 3$, combining the like terms $4y$ and $-2y$ into $2y$ allows you to isolate the variable and solve for the range of values of $y$ that satisfy the inequality.

Related terms

Coefficient:

The numerical factor that multiplies a variable in an algebraic expression.

Variable:

A symbol, usually a letter, that represents an unknown or changeable quantity in an algebraic expression.

Algebraic Expression: A mathematical phrase that combines numbers, variables, and operations, such as addition, subtraction, multiplication, and division.