## 1. Which of the following is a binomial?

### Answer:

### Explanation:

A binomial consists of two terms. In this case, x and 2y.

## 2. What is the coefficient of x in the expression 3x^2 – 5x + 7?

### Answer:

### Explanation:

The coefficient of x is the number that multiplies the variable x. In this expression, -5 multiplies x.

## 3. If (a + b)^2 = a^2 + b^2 + 2ab, then (2 + 3)^2 is:

### Answer:

### Explanation:

Using the given identity, (2 + 3)^2 = 2^2 + 3^2 + 2(2)(3) = 25.

## 4. The algebraic expression for the statement "y subtracted from 5" is:

### Answer:

### Explanation:

The statement is asking for y to be subtracted from 5, which is represented as 5 – y.

## 5. Which of the following is a polynomial?

### Answer:

### Explanation:

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms. Here, x^2 + 2x – 3 satisfies that definition.

## 6. The product of (x + 3) and (x – 3) is:

### Answer:

### Explanation:

Using the identity (a+b)(a-b) = a^2 – b^2, we get (x+3)(x-3) = x^2 – 9.

## 7. Which of the following is not an algebraic identity?

### Answer:

### Explanation:

The correct identity for (a+b)^2 is a^2 + 2ab + b^2.

## 8. Which of the following expressions has a degree of 2?

### Answer:

### Explanation:

The degree of an expression is the highest power of its variable. In 4x^2y + y^2, the highest power is 2.

## 9. The value of (a+b)(a-b) is:

### Answer:

### Explanation:

Using the identity (a+b)(a-b) = a^2 – b^2.

## 10. If p(x) = 3x^3 – x^2 + 4x – 7, then the degree of p(x) is:

### Answer:

### Explanation:

The degree is the highest power of x in the polynomial. Here, the highest power of x is 3.

## 11. The constant term in the expression 4x^2 – 3x + 2 is:

### Answer:

### Explanation:

The constant term is the term without a variable. In this expression, it's 2.

## 12. The sum of the coefficients in the expression 5x^3 – 4x^2 + 3x – 6 is:

### Answer:

### Explanation:

The coefficients are 5, -4, 3, and -6. Their sum is -2.

## 13. If (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca, what is (2 + 3 + 4)^2?

### Answer:

### Explanation:

Using the given identity, (2 + 3 + 4)^2 = 2^2 + 3^2 + 4^2 + 2(2*3) + 2(3*4) + 2(4*2) = 81.

## 14. The expression formed by subtracting 3 from 4x is:

### Answer:

### Explanation:

Subtracting 3 from 4x gives 4x – 3.

## 15. Which of the following is a term?

### Answer:

### Explanation:

A term is a single mathematical expression. x^2 is an example.

## 16. The product of (x + 5) and (x – 5) is:

### Answer:

### Explanation:

Using the identity (a+b)(a-b) = a^2 – b^2, we get (x+5)(x-5) = x^2 – 25.

## 17. An algebraic expression that has no like terms and cannot be simplified further is:

### Answer:

### Explanation:

2x and y are not like terms and cannot be combined further.

## 18. The expression x^2y^2 is an example of:

### Answer:

### Explanation:

The expression x^2y^2 has only one term, making it a monomial.

## 19. The expression 3x^2 – 4x + 7 is a:

### Answer:

### Explanation:

The expression has three terms, making it a trinomial.

## 20. If (x + y)^2 = x^2 + y^2 + 2xy, then (3 + 4)^2 is:

### Answer:

### Explanation:

Using the given identity, (3 + 4)^2 = 3^2 + 4^2 + 2(3)(4) = 49.