Algebraic expressions and identities hard

Algebraic Expressions and Identities Quiz

1. Factorize the expression: x³ - y³

a) (x - y)³ b) (x + y)³ c) (x - y)(x² + xy + y²) d) (x + y)(x² - xy + y²)

2. Expand the expression: (2x - 3y)²

a) 4x² - 6xy + 9y² b) 4x² - 12xy + 9y² c) 4x² - 6xy - 9y² d) 4x² - 9y²

3. Simplify the expression: (a² + ab + b²) - (a - b)²

a) 3ab b) a² + 2ab + b² c) -ab d) a² - ab + b²

4. Which of the following is a perfect cube?

a) 8x² b) 27y³ c) 4z² d) 5w³

5. Which of the following expressions is a difference of squares?

a) x² - 9 b) 4a² - 1 c) 9x² + 4y² d) 16b² - 25

6. Simplify the expression: (2a - 3b)³

a) 8a³ - 27b³ b) 8a³ + 27b³ c) 8a³ - 9b³ d) 8a³ + 9b³

7. Factorize the expression: 4x² - 12xy + 9y²

a) (2x - 3y)² b) (2x + 3y)² c) (2x - 3y)(2x + 3y) d) (2x + 3y)(4x - 9y)

8. Which of the following expressions is an identity?

a) (a + b)² = a² + 2ab + b² b) a² - b² = (a + b)(a - b) c) (a + b)² = a² - 2ab + b² d) a² + b² = a² - b²

9. Simplify the expression: (a + b + c)² - (a - b - c)²

a) 4ab + 4bc + 4ca b) 4ab - 4bc - 4ca c) 4a² + 4b² + 4c² d) 4a² - 4b² - 4c²

10. Factorize the expression: x³ - 8

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