Difference of Squares

This identity rewrites the difference between two squared quantities as a product of their sum and difference. It works because multiplying (a+b)(a-b) gives a^2 - ab + ab - b^2, and the middle terms cancel. That cancellation is why any pair of perfect squares with subtraction can be factored this way.

Use this when you see one square being subtracted from another, especially in algebraic factoring problems. It is also useful for simplifying expressions, solving equations, and mental arithmetic with numbers near each other.

• adding the squares instead of subtracting them
• forgetting that both terms must be perfect squares before using the pattern
• writing (a-b)(a-b) instead of (a+b)(a-b)