${\left(a+b\right)}^2=a^2+2ab+b^2$  

 

a)

${\left(\underset{a}{\underbrace{x}}+\underset{b}{\underbrace{5}}\right)}^2=x^2+2\cdot x\cdot 5+5^2=x^2+10x+25$   

 

b)

${\left(\underset{a}{\underbrace{2x}}+\underset{b}{\underbrace{7}}\right)}^2={\left(2x\right)}^2+2\cdot 2x\cdot 7+7^2=4^2+28x+49$    

 

c)

${\left(\underset{a}{\underbrace{9y}}+\underset{b}{\underbrace{8z}}\right)}^2={\left(9y\right)}^2+2\cdot 9y\cdot 8z+{\left(8z\right)}^2=81y^2+144yz+64z^2$   

 

d)

${\left(\underset{a}{\underbrace{\frac{1}{2}}}+\underset{b}{\underbrace{b}}\right)}^2={\left(\frac{1}{2}a\right)}^2+2\cdot \frac{1}{2}a\cdot b+b^2=\frac{1}{4}{a}^2+ab+b^2$   

 

e)

${\left(\underset{a}{\underbrace{\sqrt{2}}}+\underset{b}{\underbrace{1}}\right)}^2={\left(\sqrt{2}\right)}^2+2\cdot \sqrt{2}\cdot 1+1^2=2+2\sqrt{2}+1=3+2\sqrt{2}$