Worksheet on Algebraic Expressions for Class 1

Solved Questions of Algebraic Expressions

1. Which of the following is equivalent to the expression 4x² - 12x + 9?

a) (2x - 3)²
b) (2x - 3) (2x + 3)
c) (2x - 3)³
d) (2x - 3) (2x² + 3)

Answer: a) (2x - 3)²

Explanation: We have, 4x² - 12x + 9,
4x² - 12x + 9 = (2x)² – 2 x (2x) x 3 + 3²

Which satisfied, a² – 2ab + b² = (a – b)² where a = 2 and b = 3
i.e., 4x² - 12x + 9 = (2x – 3)²

2. What is the degree of the polynomial 3x³ + 5x² - 2x + 1?

a) 1
b) 2
c) 3
d) 4

Answer: c) 3

Explanation: The degree of an algebraic expression is the highest power of the variables. Hence the degree of the expression is 3.

3. Which of the following is equivalent to the expression x² + 2x + 1?

a) (2x - 3)²
b) (2x + 3)²
c) (x - 1)²
d) (x + 1)²

Answer: d) (x + 1)²

Explanation: We have, x² + 2x + 1,
x² + 2x + 1 = x² + 2 × x × 1 + 1²

Which satisfied, a² + 2ab + b² = (a + b)² where a = x and b = 1
i.e., x² + x + 1 = (x + 1)²

4. Which is the simplified form of the expression (2x – 5) (3x² + 7x)?

a) x³ - x² - 5x
b) 5x³ - 6x² + 5x
c) 6x³ - x² - 35x
d) 6x³ + x² - 5x

Answer: c) 6x³ - x² - 35x

Explanation: we have, (2x - 5) (3x² + 7x)
= 2x (3x² + 7x) – 5(3x² + 7x)
= (6x³ + 14x²) - (15x² + 35x)
= 6x³ + (14x² - 15x²) - 35x
= 6x³ - x² - 35x

5. What is the simplified form of the expression (x³ - 1) / (x - 1)?

a) x² - x +1
b) x² + x +1
c) x² + x -1
d) x² - x -1

Answer: b) x² + x +1

Explanation: we have, (x³ - 1) / (x - 1)
which follows a³ - b³ = (a - b) (a² + ab + b²)
= (x - 1) (x² + x + 1) / (x - 1)
= x² + x + 1

Practice Questions of Algebraic Expressions

1. What is the sum of the coefficients in the expansion of (x + 1)³?

a) 6
b) 7
c) 8
d) 9

Answer: c) 8

2. Which of the following is a factor of the expression x³ - 27?

a) (x - 3)
b) (x + 3)
c) (x² + 3)
d) (x² - 3x + 9)

Answer: a) (x - 3)

3. Which of the following is equivalent to the expression x³ + x² - 4x - 4?

a) (2x - 1) (x + 4) (x - 1)
b) (x - 2) (x² + 3x + 2)
c) (2x + 1) (x + 2) (x - 2)
d) (x + 1) (x² + 2x - 4)

Answer: b) (x - 2) (x² + 3x + 2)

4. What is the degree of the expression 3x⁴ + 2x² - 5x + 1?

a) 4
b) 3
c) 2
d) 1

Answer: a) 4

5. What is the coefficient of x² in the following expression (x² – 3)³?

a) -27
b) -9
c) 9
d) 27

Answer: d) 27

6. What is the value of (a² - b²) / (a - b) when a = 5 and b = 3?

a) 8
b) 10
c) 12
d) 14

Answer: a) 8

7. What is the simplified form of (x² - 4) / (x + 2)?

a) x - 2
b) x + 2
c) x² + 2x + 4
d) x + 4

Answer: a) x - 2

8. What is the product of (x - 3) (x + 5)?

a) x² - 2x - 15
b) x² + 2x + 15
c) x² + 2x - 15
d) x² - 2x + 15

Answer: c) x² + 2x - 15

9. What is the simplified form of (2x² + 3x - 1) + (3x² - 2x + 4)?

a) 5x² + x + 3
b) 5x² + x - 3
c) 5x² - 5x + 3
d) 5x² - 5x - 3

Answer: a) 5x² + x + 3

10. What is the value of the expression 2(x² + 3) + 6x – 2, if x = -2?

a) 3
b) 2
c) 1
d) 0

Answer: d) 0