The difference of squares is expressed as:

$a^2 - b^2 = (a + b)(a - b)$

Explanation:

This factorization relies on the observation that the cross terms cancel out when you expand the expression on the right:

$(a + b)(a - b) = a^2 - ab + ab - b^2 = a^2 - b^2$

Key Properties:

1. The difference of squares formula applies only when subtracting squares.
2. Both terms $a^2$ and $b^2$ must be perfect squares for clean factorization using this formula.
3. It can simplify complex polynomial expressions and solve certain types of equations efficiently.

Would you like more examples or additional explanations?

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Related Questions:

1. How does the difference of squares apply to solving quadratic equations?
2. What are some real-world applications of the difference of squares formula?
3. How can the difference of squares be extended to higher dimensions or more complex forms?
4. How is this formula used in algebraic proofs or derivations?
5. Can the difference of squares method be visualized geometrically?

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Tip:

Always check if an expression is a difference of squares before attempting more complex factorizations.