Factor completely:

(i)

$9x^{2}$ + 24xy + $16y^{2}$

Answer

(3x + 4y)^2

(ii)

$4s^{2}$ + 20st + $25t^{2}$

Answer

(2s + 5t)^2

(iii)

$49x^{2}$ + 28xy + $4y^{2}$

Answer

(7x + 2y)^2

(iv)

$64p^{2}$ + 32/3 pq + 4/9 $q^{2}$

Answer

(8p + 2/3 q)^2

(v)

$3a^{2}$ + 4ab + 4/3 $b^{2}$ (Hint: 2 was taken out as a common factor in Example 7. Is it possible to do something similar in Exercises (v) and (vi) above?)

Answer

1/3(3a + 2b)^2

(vi)

9/5 $s^{2}$ + 6sv + $5v^{2}$ (Hint: 2 was taken out as a common factor in Example 7. Is it possible to do something similar in Exercises (v) and (vi) above?)

Answer

1/5(3s + 5v)^2

Explanation

Each expression can be compared with the identity (a + b)^2 = $a^{2}$ + 2ab + $b^{2}$ . For parts (v) and (vi), following the hint similar to Example 7, we take out a common factor to make the expression fit the perfect square identity, then factor accordingly.