a.
x² + 6x +9
= x² + 2.3.x + 3²
= (x+3)²
b.
4x² + 4x +1
= (2x)² + 2.2x.1 + 1²
= (2x+1)²
c.
9x² + 12x + 4
= (3x)² + 2.2.3x + 2²
= (3x + 2)²
d.
$\frac{1}{16}$ a² + ab² + 4$b^{4}$
= ($\frac{1}{4}$ a)² + $\frac{1}{4}$ .a.2.2.b² + (2b²)²
= ($\frac{1}{4}$ a + 2b²)²
e.
16x² - 24x +9
= (4x)² - 2.4.3x + 3²
= (4x -3)²