Expand the following using the identity $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$:

(A) $(p + 3q + 7r)^2$

(B) $(3x - 2y + 4z)^2$                                                  [Page No. 77]

(A) Here, $a = p, b = 3q, c = 7r$

Using the identity:

$$\begin{aligned} (a + b + c)^2 &= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \\ (p + 3q + 7r)^2 &= p^2 + 9q^2 + 49r^2 + 6pq + 42qr + 14pr \end{aligned}$$

(B) Here, $a = 3x, b = -2y, c = 4z$

Using the identity:

$$\begin{aligned} (a + b + c)^2 &= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \\ (3x - 2y + 4z)^2 &= 9x^2 + 4y^2 + 16z^2 - 12xy - 16yz + 24xz \end{aligned}$$