Simplify Algebraic Expressions

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What is an algebraic expression?

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An algebraic expression is a mathematical phrase that includes numbers, variables, and operations (like addition, subtraction, multiplication, and division).

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How do you identify the terms in an algebraic expression?

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Terms in an algebraic expression are separated by plus (+) or minus (-) signs. Each term can be a number, a variable, or a combination of both.

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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 in an algebraic expression. For example, in 4x, 4 is the coefficient.

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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 perform any operations to make the expression as concise as possible.

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What are like terms?

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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. For example, 2(x + 3) = 2x + 6.

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What is the perimeter of a rectangle?

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The perimeter of a rectangle is the total distance around it, calculated as P = 2(length + width).

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How do you write an expression for the perimeter of a rectangle with length 'y' and width 'y-2'?

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The expression for the perimeter is P = 2(y + (y - 2)) = 4y - 4.