Question 27

A and D are algebraic expressions.

Both 2(x + 3) + 4 and 4y ^ 2 + 2y – 3 are algebraic expressions, as they consist of variables, coefficients, and constants combined using arithmetic operations.

A) 2(x + 3) + 4

This option is an algebraic expression because it includes a variable (x), coefficients (2 and 4), and is structured with addition and multiplication. Algebraic expressions can be simplified but do not contain equality or inequality signs.

B) 4 = x ^ 2

This option is not an algebraic expression; rather, it is an equation. It states that 4 is equal to x squared, which implies a relationship between the two sides rather than simply expressing a value or quantity.

C) x = 3y + 7

This option is also not an algebraic expression, but an equation. It defines a relationship where the variable x is expressed as a function of y, indicating that it is equal to the expression on the right side rather than being a standalone expression.

D) 4y ^ 2 + 2y – 3

This option is an algebraic expression as it consists of variable y raised to a power, coefficients (4 and 2), and a constant (–3), combined using addition and subtraction. It represents a polynomial expression and does not imply any equality.

Conclusion

In summary, options A and D qualify as algebraic expressions because they represent combinations of variables and constants without asserting equality. Options B and C fail to meet the criteria for algebraic expressions as they represent equations, which express relationships rather than standalone mathematical expressions.