1. The problem is to find numbers that satisfy a given identity. 2. First, identify the identity or equation you are working with. For example, if the identity is $a^2 - b^2 = (a-b)(a+b)$, we want to find numbers $a$ and $b$ that satisfy this. 3. The formula used depends on the identity. For the difference of squares, the formula is $a^2 - b^2 = (a-b)(a+b)$. 4. Important rules: the identity must hold true for the numbers chosen, meaning both sides of the equation must be equal. 5. To find numbers that work, pick values for $a$ and $b$ and verify the identity. 6. For example, let $a=5$ and $b=3$: - Calculate left side: $5^2 - 3^2 = 25 - 9 = 16$ - Calculate right side: $(5-3)(5+3) = 2 \times 8 = 16$ 7. Since both sides equal 16, $a=5$ and $b=3$ satisfy the identity. 8. You can try other pairs similarly to find more numbers that work. Final answer: Numbers like $a=5$ and $b=3$ satisfy the identity $a^2 - b^2 = (a-b)(a+b)$.