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Questions and Answers
What is an algebraic expression?
What is an algebraic expression?
- A single number
- A combination of letters and numbers with no operations
- An equation with equal signs
- A combination of variables, numbers, and at least one operation (correct)
What is the simplest form of an algebraic expression?
What is the simplest form of an algebraic expression?
An algebraic expression has no like terms and no parentheses.
What is the Distributive Property?
What is the Distributive Property?
a(b + c) = ab + ac
What are equivalent expressions?
What are equivalent expressions?
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What is a term in algebraic expressions?
What is a term in algebraic expressions?
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What is a coefficient?
What is a coefficient?
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What are like terms?
What are like terms?
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What is a constant term?
What is a constant term?
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Identify the terms in the expression 6n - 7n - 4 + n.
Identify the terms in the expression 6n - 7n - 4 + n.
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What does it mean to simplify an algebraic expression?
What does it mean to simplify an algebraic expression?
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The expression 7x - 2 - 7x + 6 simplifies to _____
The expression 7x - 2 - 7x + 6 simplifies to _____
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Study Notes
Algebraic Expressions
- An algebraic expression consists of variables, numbers, and at least one operation (addition, subtraction, multiplication, or division).
Simplest Form
- An algebraic expression is in simplest form if it contains no like terms and no parentheses.
- The Distributive Property is used to combine like terms, which is known as simplifying the expression.
Distributive Property
- Mathematically expressed as a(b + c) = ab + ac.
- Example: 2(4 + 3) simplifies to 2(4) + 2(3).
Equivalent Expressions
- Expressions that yield the same solutions are termed equivalent expressions.
- Example: 2(x + 3) and 2x + 6 are equivalent.
Term
- A term is defined as a number, a variable, or the product of a number and a variable.
Coefficient
- A coefficient is the number or symbol that multiplies a variable or an unknown quantity in an algebraic term.
Like Terms
- Like terms share the same variable and exponent, making them compatible for combining.
Constant
- A constant is a term without a variable; constant terms are also considered like terms.
Identifying Parts of an Expression
- Given the expression 6n - 7n - 4 + n:
- Terms: 6n, -7n, -4, n
- Coefficients: 6, -7, 1
- Like terms: 6n, -7n, n
- Constant: -4
Simplifying an Algebraic Expression
- Simplifying involves writing the expression in a compact form by collecting like terms.
- Only like terms can be combined, and the Distributive Property is essential for this process.
- Example of simplification:
- Start with 7x - 2 - 7x + 6.
- Combine like terms: (7x - 7x) + (-2 + 6) leads to 0x + 4, ultimately simplifying to 4.
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