Simplifying Algebraic Expressions Flashcards

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Questions and Answers

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?

An algebraic expression has no like terms and no parentheses.

What is the Distributive Property?

a(b + c) = ab + ac

What are equivalent expressions?

<p>Equations that have exactly the same solutions.</p> Signup and view all the answers

What is a term in algebraic expressions?

<p>A number, a variable, or the product of a number and a variable.</p> Signup and view all the answers

What is a coefficient?

<p>The number or symbol multiplied with a variable.</p> Signup and view all the answers

What are like terms?

<p>Terms that have the same variable and the same exponent.</p> Signup and view all the answers

What is a constant term?

<p>A term without a variable.</p> Signup and view all the answers

Identify the terms in the expression 6n - 7n - 4 + n.

<p>Terms: 6n, -7n, -4, n.</p> Signup and view all the answers

What does it mean to simplify an algebraic expression?

<p>Writing it in the most compact manner without changing its value.</p> Signup and view all the answers

The expression 7x - 2 - 7x + 6 simplifies to _____

<p>4</p> Signup and view all the answers

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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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