Factor completely:

(A) $9x^2 + 24xy + 16y^2$

(B) $4s^2 + 20st + 25t^2$

(C) $49x^2 + 28xy + 4y^2$

(D) $64p^2 + \frac{32}{3}pq + \frac{4}{9}q^2$

* (E) $3a^2 + 4ab + \frac{4}{3}b^2$

* (F) $\frac{9}{5}s^2 + 6sv + 5v^2$                                     [Page No. 74]

(A) $(3x)^2 + 2(3x)(4y) + (4y)^2 = (3x + 4y)^2$

(B) $(2s)^2 + 2(2s)(5t) + (5t)^2 = (2s + 5t)^2$

(C) $(7x)^2 + 2(7x)(2y) + (2y)^2 = (7x + 2y)^2$

(D) $(8p)^2 + 2(8p)\left(\frac{2q}{3}\right) + \left(\frac{2q}{3}\right)^2 = \left(8p + \frac{2q}{3}\right)^2$

(E) Take $\frac{1}{3}$ common from given expression:

$3a^2 + 4ab + \frac{4}{3}b^2$

$= \frac{1}{3}[9a^2 + 12ab + 4b^2]$

$= \frac{1}{3}[(3a)^2 + 2(3a)(2b) + (2b)^2]$

$= \left(\frac{1}{3}\right)(3a + 2b)^2$

(F) Take $\frac{1}{5}$ common from given expression:

$= \left(\frac{1}{5}\right)[9s^2 + 30sv + 25v^2]$

$= \left(\frac{1}{5}\right)[(3s)^2 + 2(3s)(5v) + (5v)^2]$

$= \left(\frac{1}{5}\right)(3s + 5v)^2$