Find each of the following products:
(i) (x + 3)(x − 3)
(ii) (2x + 5)(2x − 5)
(iii) (8 + x)(8 − x)
(iv) (7x + 11y)(7x − 11y)
(v) $\left(5 x^{2}+\frac{3}{4} y^{2}\right)\left(5 x^{2}-\frac{3}{4} y^{2}\right)$
(vi) $\left(\frac{4 x}{5}-\frac{5 y}{3}\right)\left(\frac{4 x}{5}+\frac{5 y}{3}\right)$
(vii) $\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)$
(viii) $\left(\frac{1}{x}+\frac{1}{y}\right)\left(\frac{1}{x}-\frac{1}{y}\right)$
(i) We have:
$(x+3)(x-3)$
$=x^{2}-9$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(ii) We have:
$(2 x+5)(2 x-5)$
$=4 x^{2}-25$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(iii) We have:
$(8+x)(8-x)$
$=64-x^{2}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(iv) We have:
$(7 x+11 y)(7 x-11 y)$
$=49 x^{2}-121 y^{2}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(v) We have:
$\left(5 x^{2}+\frac{3}{4} y^{2}\right)\left(5 x^{2}-\frac{3}{4} y^{2}\right)
$=25 x^{4}-\frac{9}{16} y^{4}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(vi) We have:
$\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)$
$=x^{2}-\frac{1}{x^{2}}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(vii) We have:
$\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)
$=x^{2}-\frac{1}{x^{2}}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
(viii) We have:
$\left(\frac{1}{x}+\frac{1}{y}\right)\left(\frac{1}{x}-\frac{1}{y}\right)$
$=\frac{1}{x^{2}}-\frac{1}{y^{2}}$$\quad\left[\operatorname{using}(a+b)(a-b)=a^{2}-b^{2}\right]$
(ix) We have:
$\left(2 a+\frac{3}{b}\right)\left(2 a-\frac{3}{b}\right)$
$=4 a^{2}-\frac{9}{b^{2}}$$\quad\left[\right.$ using $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$