What if we replace $b$ by $-b$  in $(a + b)^2 = a^2 + 2ab + b^2$ ?                            [Page No. 73]

To obtain the identity for the square of a difference, replace $b$ by $(-b)$ in the identity

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

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

Since, $2a(-b) = -2ab$ and $(-b)^2 = b^2$, we get

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

$$\text{Thus, } (a - b)^2 = a^2 - 2ab + b^2$$

Observe that compared to the identity $(a + b)^2 = a^2 + 2ab + b^2$, only the sign of the middle term changes.