$a)x^2+6x+9=x^2+2\cdot x\cdot 3+3^2={\left(x+3\right)}^2$

 

$b)25x^2+70x+49={\left(5x\right)}^2+2\cdot 5x\cdot 7+7^2={\left(5x+7\right)}^2$

 

$c)\frac{1}{4}{k}^2+k+1={\left(\frac{1}{2}k\right)}^2+2\cdot \frac{1}{2}k\cdot 1+1^2={\left(\frac{1}{2}k+1\right)}^2$