(A) What can you say about $a$ and $b$ if $(a + b)^2 < a^2 + b^2$ ?

(B) What can you say about $a$ and $b$ if $(a + b)^2 > a^2 + b^2$ ?

(C) When will $(a + b)^2$ be equal to $a^2 + b^2$ ?
 Did you observe that $(a + b)^2$ and $a^2 + b^2$ are both positive? What term will decide which is larger? Use the expansion of $(a + b)^2$ to decide.                   [Page No. 71]

Expand and subtract: $(a + b)^2 - (a^2 + b^2) = (a^2 + 2ab + b^2) - (a^2 + b^2) = 2ab$.
So, the single term $2ab$ decides everything.

Thus, the sign of $2ab$ determines the relationship:

(A) If $ab < 0$ (opposite signs), then $(a + b)^2 < a^2 + b^2$.

(B) If $ab > 0$ (same sign), then $(a + b)^2 > a^2 + b^2$.

(C) If $ab = 0$ (at least one number is 0), then $(a + b)^2 = a^2 + b^2$.

Hence, the comparison depends entirely on the product $ab$.