Algebraic Proofs

Math ⇒ Algebra

Algebraic Proofs starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Algebraic Proofs. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 8

If a = 2 and b = 3, prove that (a + b)² - (a - b)² = 4ab.

If a = 3 and b = 2, prove that (a + b)² = a² + 2ab + b².

If a = 4 and b = 1, prove that (a + b)² - (a - b)² = 4ab.

If a = 5 and b = 2, prove that a² - b² = (a - b)(a + b).

If x + 3 = 7, prove that x = 4.

If x = 2 and y = 5, prove that xy + x + y = (x + 1)(y + 1) - 1.

If x = 3 and y = 4, prove that (x + y)² = x² + 2xy + y².

Prove that for any integer n, n(n + 1) is always even.

Prove that for any integer n, n² + n is always even.

Prove that if x is a multiple of 4, then x is also a multiple of 2.

Prove that if x is an odd number, then x² is also odd.

Prove that if x is divisible by 6, then x is divisible by both 2 and 3.

Prove that the product of two odd numbers is always odd.

Prove that the sum of any two even numbers is always even.

Prove that the sum of the first n odd numbers is n².

Prove that the sum of three consecutive integers is always divisible by 3.