Algebraic Expressions

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What is an algebraic expression?

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An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It does not have an equality sign.

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What is the difference between a term and a coefficient in an algebraic expression?

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A term is a single mathematical expression that can be a number, a variable, or a combination of both multiplied together. A coefficient is a numerical factor that multiplies a variable in a term.

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How do you evaluate an algebraic expression?

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To evaluate an algebraic expression, substitute the values of the variables into the expression and perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).

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What does it mean to simplify an algebraic expression?

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Simplifying an algebraic expression means to combine like terms and reduce the expression to its simplest form.

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What is the order of operations in mathematics?

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The order of operations is a set of rules that determines the sequence in which calculations are performed. The order is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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What is a polynomial?

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A polynomial is an algebraic expression that consists of one or more terms, where each term is a product of a constant and a variable raised to a non-negative integer exponent.

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What is the difference between a monomial, binomial, and trinomial?

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A monomial has one term, a binomial has two terms, and a trinomial has three terms.

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How do you factor a difference of squares?

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To factor a difference of squares, use the formula a² - b² = (a + b)(a - b).

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What is the value of an expression when a = 4 and b = 2 in a² - b²?

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The value is 12, calculated as 4² - 2² = 16 - 4 = 12.

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How do you evaluate the expression 6 + 7b - 3a for a = 2 and b = 8?

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Substituting the values gives 6 + 7(8) - 3(2) = 6 + 56 - 6 = 56.