1. Which of the following are algebraic expressions? Select ALL that apply.
Answer: A,D
A and D are algebraic expressions.
Both options A and D represent algebraic expressions, where A is a combination of variables and constants multiplied and added together, and D is a polynomial expression composed of terms with variables raised to powers.
A) 2 * (x + 3) + 4
Option A is an algebraic expression because it consists of a variable \( x \) combined through addition and multiplication with constants. It can be simplified and expressed in polynomial form, which is a key characteristic of algebraic expressions.
B) 4 = x ^ 2
Option B is not an algebraic expression; instead, it is an equation. An equation asserts that two expressions are equal, but does not itself represent a single algebraic expression. Therefore, it does not fit the criteria of being an algebraic expression.
C) x = 3y + 7
Option C is also not an algebraic expression; like Option B, it is an equation. It indicates that \( x \) is equal to the expression \( 3y + 7 \), rather than being a standalone expression. Thus, it cannot be classified as an algebraic expression.
D) 4y ^ 2 + 2y - 3
Option D is an algebraic expression as it is a polynomial consisting of multiple terms with different powers of the variable \( y \). This fits the definition of an algebraic expression, making it valid.
Conclusion
In summary, options A and D are both algebraic expressions due to their structure involving the combination of variables and constants. Options B and C fail to qualify as they present equations rather than expressions, which highlights the importance of distinguishing between these fundamental algebraic concepts.