10 Questions
What is the first step in the process of combining like terms?
Identifying like terms
Which of the following best describes like terms in algebra?
Terms that have the same variable and the same exponent
What does combining constants involve in algebraic expressions?
Adding or subtracting constants that do not have a variable
In the expression 3x^2 + 2x^2 + 4x^2, what is the result of combining the like terms?
$9x^2$
Which technique is essential for simplifying expressions and solving equations?
Combining like terms
What is the simplified expression of $5x^2 + 4x^2 - 2x^2$?
$6x^2$
In the equation $4x - 2 = 3x + 5$, what is the combined constant on the left side of the equation?
$-7$
In the expression $7y^2 + 3y^2 - 5y^2$, what is the simplified form?
$-5y^2$
What is the result of combining like terms in the expression $-3a + 5a - 2a$?
$4a$
In the equation $8y - 3 = 2y + 4$, what is the combined constant on the right side of the equation?
$4$
Study Notes
Combining like terms is a fundamental algebraic technique that involves adding or subtracting terms that have the same variable and the same exponent. This technique is essential for simplifying expressions and solving equations. In this article, we will discuss the process of combining like terms, including identifying like terms, combining constants, combining variables, simplifying expressions, and applications of combining like terms.
Identifying Like Terms
Identifying like terms is the first step in the process of combining like terms. Like terms are terms that have the same variable and the same exponent. For example, in the expression 3x^2 + 2x^2 + 4x^2, the terms 3x^2, 2x^2, and 4x^2 are like terms because they all have the variable x and the exponent 2.
Combining Constants
Combining constants is a simple process that involves adding or subtracting constants that do not have a variable. For example, in the expression 5x + 3 + 2x - 4, the constants 3 and -4 can be combined to give the result 3 - 4 = -1.
Combining Variables
Combining variables involves adding or subtracting terms that have the same variable and the same exponent. For example, in the expression 3x^2 + 2x^2 + 4x^2, the like terms 3x^2, 2x^2, and 4x^2 can be combined to give the result 3x^2 + 2x^2 + 4x^2 = 9x^2.
Simplifying Expressions
Simplifying expressions involves combining like terms to reduce the complexity of the expression. For example, in the expression 3x^2 + 2x^2 + 4x^2, combining the like terms gives the simplified expression 9x^2.
Applications of Combining Like Terms
Combining like terms is a technique that has many applications in algebra, including solving equations and simplifying expressions. For example, in the equation 3x + 2 = 5x - 4, combining like terms on the left side of the equation gives the simplified equation 3x + 2 = 5x - 4 => 3x - 5x + 2 = -4 => -2x - 4 = -4 => x = 2.
In conclusion, combining like terms is a fundamental algebraic technique that is essential for simplifying expressions and solving equations. By identifying like terms, combining constants, combining variables, and simplifying expressions, we can reduce the complexity of algebraic expressions and solve equations more efficiently.
Explore the fundamental algebraic technique of combining like terms, which involves simplifying expressions and solving equations by identifying like terms, combining constants, combining variables, simplifying expressions, and discussing applications of the technique. Learn to recognize like terms, combine constants and variables, simplify expressions, and apply the method to solve equations.
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