Which of the following are algebraic expressions? Select ALL that apply.

Rationale

2(x + 3) + 4 and 4y ^ 2 + 2y – 3 are algebraic expressions.

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators, but do not contain an equality sign. Choices A and D fit this definition as they express quantities without equating them to anything.

A (2(x + 3) + 4) CORRECT

This choice is an algebraic expression because it combines constants and variables through addition and multiplication without implying any equality. It represents a mathematical quantity that can be simplified but does not equate to another expression or number.

B (4 = x ^ 2) YOUR ANSWER

This choice is not an algebraic expression but an equation since it includes an equality sign. It states that 4 is equal to \(x^2\), making it a statement rather than a mere expression.

C (x = 3y + 7) YOUR ANSWER

Similar to choice B, this option is an equation and not an algebraic expression because it contains an equality sign. It expresses a relationship between \(x\) and \(y\) rather than merely representing a mathematical quantity.

D (4y ^ 2 + 2y – 3) CORRECT

This choice is an algebraic expression as it consists of terms combined through addition and subtraction, involving constants and variables, without any equality sign. It describes a mathematical quantity that can be evaluated for different values of \(y\).

Conclusion

Algebraic expressions are formed from variables, constants, and mathematical operations, lacking any equality sign. In this question, options A and D qualify as algebraic expressions, while options B and C are equations, thus disqualifying them from the category of expressions. Understanding the distinction between expressions and equations is fundamental in algebra, facilitating clearer communication of mathematical ideas.

Which of the following are algebraic expressions? Select ALL that apply.

2(x + 3) + 4 and 4y ^ 2 + 2y – 3 are algebraic expressions.

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