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Questions and Answers
How can we rewrite the expression $5(x + 2)$ using the distributive property?
How can we rewrite the expression $5(x + 2)$ using the distributive property?
- $5x + 10$ (correct)
- $5x + 2$
- $5x + 5$
- $10x$
What is the result of simplifying the expression $x^2 - 3x + 5 - 2x^2 + 4x - 3$?
What is the result of simplifying the expression $x^2 - 3x + 5 - 2x^2 + 4x - 3$?
- $-x^2 + 7x + 2$ (correct)
- $-x^2 + x + 7$
- $-3x^2 + x + 2$
- $-2x^2 + 7x - 1$
In the expression $5x + 2x$, what is the result of combining like terms?
In the expression $5x + 2x$, what is the result of combining like terms?
- $7x$ (correct)
- $3x$
- $10$
- $10x$
Which property is used to expand expressions like $3(4x + 2)$?
Which property is used to expand expressions like $3(4x + 2)$?
What should be done first to simplify a complex algebraic expression?
What should be done first to simplify a complex algebraic expression?
When subtracting algebraic expressions, what is the first step to take?
When subtracting algebraic expressions, what is the first step to take?
In the expression $2x^2 - 3x + 5$, which term should be rearranged and have its sign changed for subtraction?
In the expression $2x^2 - 3x + 5$, which term should be rearranged and have its sign changed for subtraction?
What is the result of simplifying $4(x + 3) - 2(x - 5)$ using the distributive property?
What is the result of simplifying $4(x + 3) - 2(x - 5)$ using the distributive property?
Which expression illustrates combining like terms correctly?
Which expression illustrates combining like terms correctly?
In the expression $7ab + 3ab$, what is the sum of these like terms?
In the expression $7ab + 3ab$, what is the sum of these like terms?
When adding algebraic expressions, what is the key method to simplify the expression?
When adding algebraic expressions, what is the key method to simplify the expression?
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Study Notes
Algebraic Expressions: Subtraction, Addition, Distributive Property, and Simplifying
Algebraic expressions are the building blocks of algebraic problem-solving, made up of variables and constants combined using the basic operations of addition, subtraction, multiplication, and division. In this article, we'll explore how to manipulate algebraic expressions during subtraction, addition, and the use of the distributive property, as well as the practice of simplifying expressions and combining like terms.
Subtraction of Algebraic Expressions
When subtracting algebraic expressions, we follow the same order of operations as with arithmetic expressions. In other words, first perform any operations within parentheses, then work with exponents, and so on. For subtracting two expressions, simply change the sign of the second expression and add it to the first one. For example, to find (x^2 - 3x - 5 - (2x^2 - 4)), rearrange the second expression as (2x^2 - 4) and change the sign:
[x^2 - 3x - 5 + (-2x^2 + 4) = x^2 - 2x^2 - 3x + 4]
Addition of Algebraic Expressions
When adding algebraic expressions, we can simply combine like terms. Like terms are terms that have the same variable raised to the same power. For example, (3x^2 + 2x^2) have a like term (3x^2 + 2x^2 = 5x^2). Similarly, (3xy + 2xy) are like terms, and so are (3x + 2x).
Distributive Property
The distributive property states that for any expressions (a, b,) and (c), (a(b + c) = ab + ac). This property allows us to expand expressions, such as (5(x + 2)). We can rewrite this as (5x + 5(2)), which equals (5x + 10).
Simplifying Expressions
Simplifying expressions means writing an expression in its most basic form, often by combining like terms or applying the order of operations. For example, to simplify (x^2 - 3x + 5 - 2x^2 + 4x - 3), group the like terms:
[x^2 - 3x + 5 - 2x^2 + 4x - 3 = -x^2 + (3 + 4)x + (5 - 3) = -x^2 + 7x + 2]
Combining Like Terms
To combine like terms, simply add their coefficients. For example, to combine (5x + 2x), the sum is (5x + 2x = 7x).
By understanding and applying these concepts, you'll be better equipped to solve more complex algebraic problems. As always, practice makes perfect, so keep solving problems and applying these techniques to improve your algebraic skills.
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