Przypomnijmy wzory skróconego mnożenia na kwadrat sumy i kwadrat różnicy: 

${\left(a+b\right)}^2=a^2+2ab+b^2$

${\left(a-b\right)}^2=a^2-2ab+b^2$

 

 

$a)x^2+12x+36=x^2+2\cdot x\cdot 6+6^2={\left(x+6\right)}^2$

$b)100k^2-40k+4={\left(10k\right)}^2-2\cdot 10k\cdot 2+2^2={\left(10k-2\right)}^2$

$c)a^2{b}^2+10ab+25={\left(ab\right)}^2+2\cdot ab\cdot 5+5^2={\left(ab+5\right)}^2$

$d)3t^2+2\sqrt{6}tu+2u^2={\left(\sqrt{3}t\right)}^2+2\cdot \sqrt{3}t\cdot \sqrt{2}u+{\left(\sqrt{2}u\right)}^2={\left(\sqrt{3}t+\sqrt{2}u\right)}^2$