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, while choices B and C are equations or statements rather than expressions.

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

This is an algebraic expression because it combines numbers and variables using addition and multiplication without an equality sign. It represents a value that changes based on the value of the variable x.

B (4 = x ^ 2) YOUR ANSWER

This choice is not an algebraic expression but rather an equation, as it contains an equality sign. It states that 4 is equal to the square of x, making it a relationship rather than a standalone expression.

C (x = 3y + 7) YOUR ANSWER

Similar to choice B, this is an equation because it includes an equality sign. It shows a relationship between the variable x and the expression on the right side (3y + 7), hence it cannot be considered an algebraic expression.

D (4y ^ 2 + 2y - 3) CORRECT

This is an algebraic expression. It consists of terms that include the variable y, combined using addition and subtraction, and does not involve an equality sign. It represents a polynomial expression that varies with the value of y.

Conclusion

Algebraic expressions are characterized by the absence of an equality sign and consist of variables, coefficients, and mathematical operations. In this case, choices A and D qualify as algebraic expressions, while B and C do not, as they represent equations that express relationships between quantities. Understanding this distinction is crucial for manipulating and solving algebraic problems effectively.

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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