a)
$\begin{array}{l} A = {\left( {5x + 5} \right)^2} + 10\left( {x - 3} \right)\left( {x + 1} \right) + {x^2} - 6x + 9\\ A = 25{\left( {x + 1} \right)^2} + 10\left( {{x^2} - 2x - 3} \right) + {x^2} - 6x + 9\\ A = 25{x^2} + 50x + 25 + 10{x^2} - 20x - 30 + {x^2} - 6x + 9\\ A = 36{x^2} + 24x + 4\\A=(6x+2)^2 \end{array}$
b)
$\begin{array}{l} B = \dfrac{{{{\left( {x - 1} \right)}^2}}}{4} + {x^2} - 1 + {\left( {x + 1} \right)^2}\\ B = \dfrac{{{x^2} - 2x + 1}}{4} + {x^2} - 1 + {x^2} + 2x + 1\\ B = \dfrac{{{x^2} - 2x + 1}}{4} + 2{x^2} + 2x\\ B = \dfrac{{9{x^2} + 6x + 1}}{4} = \dfrac{{{{\left( {3x + 1} \right)}^2}}}{4} \end{array}$
c)
$\begin{array}{l} C = {\left( {x - y - z} \right)^2} + 2\left( {x - y - z} \right)\left( {y + z} \right) + {\left( {y + z} \right)^2}\\ C = {\left( {x - y - z + y + z} \right)^2} = {x^2} \end{array}$
