1. **State the problem:** Solve the equation $a^2 = 2a \times a + b$ for $b$. 2. **Rewrite the equation:** The equation is given as $$a^2 = 2a \times a + b$$ 3. **Simplify the right side:** Multiply $2a$ and $a$: $$2a \times a = 2a^2$$ 4. **Substitute back:** $$a^2 = 2a^2 + b$$ 5. **Isolate $b$:** Subtract $2a^2$ from both sides: $$a^2 - 2a^2 = b$$ 6. **Simplify the left side:** $$\cancel{a^2} - 2\cancel{a^2} = b$$ $$-a^2 = b$$ 7. **Final answer:** $$b = -a^2$$ This means $b$ is the negative of $a$ squared.