Section 1
Difference of Squares Pattern
Property
Difference of Two Squares.
In this Grade 4 AMC math lesson from AoPS: Introduction to Algebra, students learn the difference of squares factorization — the identity a² − b² = (a − b)(a + b) — and practice applying it to expressions like 4t² − 121 and z⁴ − 1. The lesson extends this technique to solving Diophantine equations by factoring expressions such as (m − n)(m + n) = 105 to find all integer solution pairs. Part of Chapter 11: Special Factorizations, this lesson builds algebraic reasoning skills essential for AMC 8 and AMC 10 competition preparation.
Section 1
Difference of Squares Pattern
Difference of Two Squares.
Section 2
Consecutive Squares and Difference Patterns
The difference between consecutive squares follows the pattern:
This means the difference between any two consecutive perfect squares is always an odd number.
Section 3
Difference of Squares Factorization
Section 4
Solving Diophantine Equations Using Difference of Squares
When a Diophantine equation can be written as , factor it as and find integer solutions by examining all factor pairs of .
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Section 1
Difference of Squares Pattern
Difference of Two Squares.
Section 2
Consecutive Squares and Difference Patterns
The difference between consecutive squares follows the pattern:
This means the difference between any two consecutive perfect squares is always an odd number.
Section 3
Difference of Squares Factorization
Section 4
Solving Diophantine Equations Using Difference of Squares
When a Diophantine equation can be written as , factor it as and find integer solutions by examining all factor pairs of .
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter