What You Need to Know

An algebraic proof shows a relationship is true for all values, not just specific numbers

Start with one side of the equation and manipulate it until it equals the other side

Common proof types include proving identities and proving number properties

Always show clear, logical steps with justification for each step

Key Vocabulary

A logical argument showing a mathematical statement is always true

An equation that is true for all values of the variable

Rewrite an expression as a product of its factors

Multiply out brackets to remove them from an expression

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

To prove that n(n+1) is always even, we note that:

n is always even n+1 is always odd one of n or n+1 must always be even, so their product is even even x odd = even

Question 2

Which is a valid first step in proving (x+3)^2 = x^2 + 6x + 9?

Substitute x = 1 Add 9 to both sides Take the square root of both sides Expand (x+3)(x+3)

Question 3

What is the purpose of using variables in an algebraic proof?

To show the result works for all numbers, not just specific values To make it harder to read To avoid using numbers To introduce unknown quantities