$\begin{align*}A&=(x+5)^2\\&=x^2+2\times 5 \times x+5^2\\&=x^2+10x+25\end{align*}$
$\quad$
$\begin{align*}B&=(x-3)^2\\&=x^2-2\times 3\times x+3^2\\&=x^2-6x+9\end{align*}$
$\quad$
$\begin{align*}C&=(x+4)(x-4)\\&=x^2-4^2\\&=x^2-16\end{align*}$
$\quad$
$\begin{align*}D&=(x+7)^2\\&=x^2+2\times 7\times x+7^2\\&=x^2+14x+49\end{align*}$
$\quad$
$\begin{align*}E&=(x-1)^2\\&=x^2-2\times 1\times x+1^2\\&=x^2-2x+1\end{align*}$
$\quad$
$\begin{align*}F&=(x-6)(x+6)\\&=x^2-6^2\\&=x^2-36\end{align*}$

$\quad$

$\begin{align*}A&=(2x+3)^2\\&=(2x)^2+2\times 3\times 2x+3^2\\&=4x^2+12x+9\end{align*}$
$\quad$
$\begin{align*}B&=(5x-4)^2\\&=(5x)^2-2\times 4\times 5x+4^2\\&=25x^2-40x+16\end{align*}$
$\quad$
$\begin{align*}C&=(3x-2)(3x+2)\\&=(3x)^2-2^2\\&=9x^2-4\end{align*}$
$\quad$
$\begin{align*}D&=(6-3x)^2\\&=6^2-2\times 6\times 3x+(3x)^2\\&=36-36x+9x^2\end{align*}$
$\quad$
$\begin{align*}E&=(1+8x)^2\\&=1^2+2\times 1\times 8x+(8x)^2\\&=1+16x+64x^2\end{align*}$
$\quad$
$\begin{align*}F&=(4x+5)(5-4x)\\&=(5+4x)(5-4x)\\&=5^2-(4x)^2\\&=25-16x^2\end{align*}$

$\quad$

$\begin{align*} A&=(4x+3)^2 \\
&=(4x)^2+2\times 4x\times 3+3^2 \\
&=16x^2+24x+9
\end{align*}$
$\quad$
$\begin{align*} B&=(6x-7)^2 \\
&=(6x)^2-2\times 6x \times 7 + 7^2 \\
&=36x^2-84x+49
\end{align*}$
$\quad$
$\begin{align*}C&=(5x+4)(5x-4) \\
&=(5x)^2-4^2 \\
&=25x^2-16
\end{align*}$
$\quad$
$\begin{align*} D&=(3x+7)^2 \\
&=(3x)^2+2\times 3x \times 7 + 7^2 \\
&=9x^2+42x+49
\end{align*}$
$\quad$
$\begin{align*} E&=(7x-5)^2 \\
&=(7x)^2-2\times 7x \times 5+5^2 \\
&=49x^2-70x+25
\end{align*}$
$\quad$
$\begin{align*} F&=(3x-5)(3x+5) \\
&=(3x)^2-5^2 \\
&=9x^2-25
\end{align*}$
$\quad$
$\begin{align*} G&=(7-4x)^2 \\
&=7^2-2\times 7 \times 4x + (4x)^2 \\
&=49-56x+16x^2
\end{align*}$
$\quad$
$\begin{align*} H&=(2x+9)^2 \\
&=(2x)^2+2\times 2x \times 9 + 9^2 \\
&=4x^2+36x+81
\end{align*}$
$\quad$
$\begin{align*} I&=(6-2x)(6+2x) \\
&=6^2-(2x)^2 \\
&=36-4x^2
\end{align*}$

$\quad$

$\begin{align*} A&=\left(x+\dfrac{1}{3}\right)^2 \\
&=x^2+2 \times x\times \dfrac{1}{3} + \left(\dfrac{1}{3}\right)^2 \\
&=x^2+\dfrac{2}{3}x + \dfrac{1}{9}
\end{align*}$
$\quad$
$\begin{align*} B&=\left(2x-\dfrac{1}{2}\right)^2 \\
&=(2x)^2-2\times 2x \times \dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2 \\
&=4x^2-2x+\dfrac{1}{4}
\end{align*}$
$\quad$
$\begin{align*} C&=\left(6x+\dfrac{2}{5}\right)\left(6x-\dfrac{2}{5}\right) \\
&=(6x)^2-\left(\dfrac{2}{5}\right)^2 \\
&=36x^2-\dfrac{4}{25}
\end{align*}$
$\quad$
$\begin{align*}D&=\left(3x+\dfrac{7}{6}\right)^2 \\
&=(3x)^2+2\times 3x \times \dfrac{7}{6}+\left(\dfrac{7}{6}\right)^2 \\
&=9x^2+7x+\dfrac{49}{36}
\end{align*}$
$\quad$
$\begin{align*} E&=\left(3x-\dfrac{4}{3}\right)^2 \\
&=(3x)^2-2\times 3x \times \dfrac{4}{3}+\left(\dfrac{4}{3}\right)^2 \\
&=9x^2-8x+\dfrac{16}{9}
\end{align*}$
$\quad$
$\begin{align*}F&=\left(\dfrac{7}{4}x+\dfrac{1}{2}\right)\left(\dfrac{7}{4}x-\dfrac{1}{2}\right) \\
&=\left(\dfrac{7}{4}x\right)^2-\left(\dfrac{1}{2}\right)^2 \\
&=\dfrac{49}{16}x^2-\dfrac{1}{4}
\end{align*}$
$\quad$
$\begin{align*} G&=\left(2x-\dfrac{5}{2}\right)^2 \\
&=(2x)^2-2\times 2x\times \dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2 \\
&=4x^2-10x+\dfrac{25}{4}
\end{align*}$
$\quad$
$\begin{align*}H&=\left(3x-\dfrac{7}{3}\right)^2 \\
&=(3x)^2-2\times 3x\times \dfrac{7}{3}+\left(\dfrac{7}{3}\right)^2 \\
&=9x^2-14x+\dfrac{49}{9}
\end{align*}$
$\quad$

$\begin{align*}A&=(2x+5)^2-(3x-4)^2\\
&=(2x)^2+2\times 5\times 2x+5^2-\left((3x)^2-2\times 3x\times 4+ 4^2\right) \\
&=4x^2+20x+25-\left(9x^2-24x+16\right) \\
&=4x^2+20x+25-9x^2+24x-16\\
&=-5x^2+44x+9\end{align*}$
$\quad$
$\begin{align*}B&=(5x+7)^2+(2x-6)^2\\
&=(5x)^2+2\times 7\times 5x+7^2+(2x)^2-2\times 6\times 2x+6^2\\
&=25x^2+70x+49+4x^2-24x+36\\
&=29x^2+46x+85\end{align*}$
$\quad$
$\begin{align*}C&=(7x+2)^2-(4x-3)(4x+3) \\
&=(7x)^2+2\times 2\times 7x+2^2-\left((4x)^2-3^2\right) \\
&=49x^2+28x+4-\left(16x^2-9\right) \\
&=49x^2+28x+4-16x^2+9\\
&=33x^2+28x+13\end{align*}$
$\quad$
$\begin{align*}D&=(3x-5)(3x+5)-(3x+5)^2\\
&=(3x)^2-5^2-\left((3x)^2+2\times 5\times 3x+5^2\right) \\
&=9x^2-25-\left(9x^2+30x+25\right) \\
&=9x^2-25-9x^2-30x-25\\
&=-30x-50\end{align*}$
$\quad$
$\begin{align*}E&=(5x-3)^2-(3x-7)^2\\
&=(5x)^2-2\times 3\times 5x+3^2-\left((3x)^2-2\times 7\times 3x+7^2\right) \\
&=25x^2-30x+9-\left(9x^2-42x+49\right) \\
&=25x^2-30x+9-9x^2+42x-49\\
&=16x^2+12x-40\end{align*}$
$\quad$
$\begin{align*}F&=(7x-3)(7x+3)-(8x+5)(8x-5) \\
&=(7x)^2-3^2-\left((8x)^2-5^2\right) \\
&=49x^2-9-\left(64x^2-25\right) \\
&=49x^2-9-64x^2+25\\
&=-15x^2+16
\end{align*}$
$\quad$