Difference Squares D6405D

1. The problem is to find the formula for the difference of squares. 2. The difference of squares formula states that for any two variables or numbers $a$ and $b$, the expression $a^2 - b^2$ can be factored. 3. The formula is: $$a^2 - b^2 = (a - b)(a + b)$$ 4. This means that the difference between the square of $a$ and the square of $b$ equals the product of the sum and difference of $a$ and $b$. 5. This formula is useful for simplifying expressions and solving equations involving squares. 6. For example, if $a=5$ and $b=3$, then: $$5^2 - 3^2 = (5 - 3)(5 + 3) = 2 \times 8 = 16$$ 7. This matches the direct calculation $25 - 9 = 16$, confirming the formula's correctness.