Simplifying 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 does it mean to simplify an algebraic expression?

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To simplify an algebraic expression means to combine like terms and reduce it to its simplest form.

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What are like terms in algebra?

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Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

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How do you combine like terms?

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To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis.

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How do you apply the distributive property to simplify expressions?

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To apply the distributive property, multiply the term outside the parentheses by each term inside the parentheses and then combine like terms.

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What is a coefficient in an algebraic expression?

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A coefficient is a numerical factor that multiplies a variable. For example, in 4x, 4 is the coefficient.

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What is a constant in an algebraic expression?

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A constant is a fixed value that does not change. For example, in the expression 3x + 5, 5 is the constant.

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What is the process for simplifying the expression -2(x + 4) - (4x + 8)?

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First, apply the distributive property: -2x - 8 - 4x - 8. Then combine like terms: -2x - 4x = -6x and -8 - 8 = -16, resulting in -6x - 16.

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What is the result of simplifying the expression 22y + 12?

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The expression 22y + 12 is already in its simplest form, as there are no like terms to combine.