$$ \hspace*{6 mm}\mathrm{1.\kern2mm\ a^2 − b^2 = (a)^2 - (b)^2 } $$
$$ \hspace*{24 mm}\mathrm{= (a - b)(a + b) } $$
     
$$ \hspace*{6 mm}\mathrm{2.\kern2mm\ (c - d)(c + d) } $$      
$$ \hspace*{6 mm}\mathrm{3.\kern2mm\ (m - n)(m + n) } $$      
$$ \hspace*{6 mm}\mathrm{4.\kern2mm\ (p - q)(p + q) } $$      
$$ \hspace*{6 mm}\mathrm{5.\kern2mm\ (x - y)(x + y) } $$      
$$ \hspace*{6 mm}\mathrm{6.\kern2mm\ a^2 − 4 = (a)^2 - (2)^2 } $$
$$ \hspace*{22 mm}\mathrm{= (a - 2)(a + 2) } $$
     
$$ \hspace*{6 mm}\mathrm{7.\kern2mm\ b^2 − 16 = (b)^2 - (4)^2 } $$
$$ \hspace*{24 mm}\mathrm{= (b - 4)(b + 4) } $$
     
$$ \hspace*{6 mm}\mathrm{8.\kern2mm\ (c - 6)(c + 6) } $$      
$$ \hspace*{6 mm}\mathrm{9.\kern2mm\ (d - 10)(d + 10) } $$      
$$ \hspace*{6 mm}\mathrm{10.\kern2mm\ (h - 15)(h + 15) } $$      
$$ \hspace*{6 mm}\mathrm{11.\kern2mm\ (m - 12)(m + 12) } $$      
$$ \hspace*{6 mm}\mathrm{12.\kern2mm\ (n - 17)(n + 17) } $$      
$$ \hspace*{6 mm}\mathrm{13.\kern2mm\ p^2 - \frac{1}{4} = (p)^2 - \Big(\frac{1}{2}\Big)^2 } $$

$$ \hspace*{25 mm}\mathrm{= \Big(p - \frac{1}{2}\Big)\Big(p + \frac{1}{2}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{14.\kern2mm\ q^2 - \frac{1}{25} = (q)^2 - \Big(\frac{1}{5}\Big)^2 } $$

$$ \hspace*{27 mm}\mathrm{= (q - \frac{1}{5})(q + \frac{1}{5}) } $$

     
$$ \hspace*{6 mm}\mathrm{15.\kern2mm\ \Big(x - \frac{1}{6}\Big)\Big(x + \frac{1}{6}\Big) } $$      
$$ \hspace*{6 mm}\mathrm{16.\kern2mm\ \Big(y - \frac{4}{5}\Big)\Big(y + \frac{4}{5}\Big) } $$      
$$ \hspace*{6 mm}\mathrm{17.\kern2mm\ \Big(y - \frac{7}{6}\Big)\Big(y + \frac{7}{6}\Big) } $$      
$$ \hspace*{6 mm}\mathrm{18.\kern2mm\ a^2 - \frac{4b^2}{81} = (a)^2 - \Big(\frac{2b}{9}\Big)^2 } $$

$$ \hspace*{29 mm}\mathrm{= \Big(a - \frac{2b}{9}\Big)\Big(a + \frac{2b}{9}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{19.\kern2mm\ x^2 - 0,01 = (x)^2 - (0,1)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (x - 0,1)(x + 0,1) } $$
     
$$ \hspace*{6 mm}\mathrm{20.\kern2mm\ (y - 0,3)(y + 0,3) } $$      
$$ \hspace*{6 mm}\mathrm{21.\kern2mm\ (z - 0,16)(z + 0,16) } $$      
$$ \hspace*{6 mm}\mathrm{22.\kern2mm\ (a - 0,4)(a + 0,4) } $$      
$$ \hspace*{6 mm}\mathrm{23.\kern2mm\ (3b - 4)(3b + 4) } $$      
$$ \hspace*{6 mm}\mathrm{24.\kern2mm\ (5c - 7)(5c + 7) } $$      
$$ \hspace*{6 mm}\mathrm{25.\kern2mm\ (4m - 7n)(4m + 7n) } $$      
$$ \hspace*{6 mm}\mathrm{26.\kern2mm\ (5n - 9p)(5n + 9p) } $$      
$$ \hspace*{6 mm}\mathrm{27.\kern2mm\ (11p - 15xy)(11p + 15xy) } $$
     
$$ \hspace*{6 mm}\mathrm{28.\kern2mm\ \frac{a^2}{16} − \frac{25}{b^2} = \Big(\frac{a}{4}\Big)^2\ ─\ \Big(\frac{5}{b}\Big)^2 } $$

$$ \hspace*{26 mm}\mathrm{= \Big(\frac{a}{4}\ ─\ \frac{5}{b}\Big)\Big(\frac{a}{4}\ +\ \frac{5}{b}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{29.\kern2mm\ \Big(\frac{3c}{4d}\ ─\ \frac{5}{9}\Big) \Big(\frac{3c}{4d}\ +\ \frac{5}{9}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{30.\kern2mm\ \Big(\frac{4x}{7y}\ ─\ \frac{9p}{11q}\Big)\Big(\frac{4x}{7y}\ +\ \frac{9p}{11q}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{31.\kern2mm\ \Big(\frac{11a}{12b}\ ─\ \frac{13c}{15d}\Big)\Big(\frac{11a}{12b}\ +\ \frac{13c}{15d}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{32.\kern2mm\ \Big(\frac{2ab}{3p}\ ─\ \frac{5cd}{4q}\Big)\Big(\frac{2ab}{3p}\ +\ \frac{5cd}{4q}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{33.\kern2mm\ 4a^2 − 3b^2 = (2a)^2 - (\sqrt{3}b)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (2a - \sqrt{3}b)(2a + \sqrt{3}b) } $$

     
$$ \hspace*{6 mm}\mathrm{34.\kern2mm\ (\sqrt{5}p - \sqrt{13}q)(\sqrt{5}p + \sqrt{13}q) } $$

     
$$ \hspace*{6 mm}\mathrm{35.\kern2mm\ (\sqrt{3}a - \sqrt{5}b)(\sqrt{3}a + \sqrt{5}b) } $$

     
$$ \hspace*{6 mm}\mathrm{36.\kern2mm\ \Big(p - \frac{q}{\sqrt{3}}\Big)\Big(p + \frac{q}{\sqrt{3}}\Big) } $$

     
$$ \hspace*{6 mm}\mathrm{37.\kern2mm\ \Big(p - \frac{\sqrt{2}q}{\sqrt{3}} \Big) \Big(p + \frac{\sqrt{2}q}{\sqrt{3}} \Big) } $$


     
$$ \hspace*{6 mm}\mathrm{38.\kern2mm\ \Big(\frac{\sqrt{3}a}{\sqrt{5}b} - \frac{\sqrt{7}p}{\sqrt{17}q} \Big) \Big(\frac{\sqrt{3}a}{\sqrt{5}b} + \frac{\sqrt{7}p}{\sqrt{17}q} \Big) } $$


     
$$ \hspace*{6 mm}\mathrm{39.\kern2mm\ a^4 − b^4 = (a^2)^2 - (b^2)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (a^2 - b^2)(a^2 + b^2) } $$
$$ \hspace*{26 mm}\mathrm{= (a - b)(a + b)(a^2 + b^2) } $$
     
$$ \hspace*{6 mm}\mathrm{40.\kern2mm\ p^4 − q^4 = (p^2)^2 - (q^2)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (p^2 - q^2)(p^2 + q^2) } $$
$$ \hspace*{26 mm}\mathrm{= (p - q)(p + q)(p^2 + q^2) } $$
     
$$ \hspace*{6 mm}\mathrm{41.\kern2mm\ p^6 − q^6 = (p^3)^2 - (q^3)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (p^3 - q^3)(p^3 + q^3) } $$
$$ \hspace*{26 mm}\mathrm{= (p - q)(p^2 + pq + q^2)(p + q)(p^2 - pq + q^2) } $$
     
$$ \hspace*{6 mm}\mathrm{42.\kern2mm\ x^8 − y^8 = (x^4)^2 - (y^4)^2 } $$
$$ \hspace*{26 mm}\mathrm{= (x^4 - y^4)(x^4 + y^4) } $$
$$ \hspace*{26 mm}\mathrm{= ((x^2)^2 - (y^2)^2)(x^4 + y^4) } $$
$$ \hspace*{26 mm}\mathrm{= (x^2 - y^2)(x^2 + y^2)(x^4 + y^4) } $$
$$ \hspace*{26 mm}\mathrm{= (x - y)(x + y)(x^2 + y^2)(x^4 + y^4) } $$
     
$$ \hspace*{6 mm}\mathrm{43.\kern2mm\ \Big(x^5 - \frac{1}{2}\Big)\Big(x^5 - \frac{1}{2}\Big) } $$      
$$ \hspace*{6 mm}\mathrm{44.\kern2mm\ x^8 − \frac{256}{6 561} = (x^4 - \frac{16}{81})(x^4 + \frac{16}{81}) } $$

$$ \hspace*{10 mm}\mathrm{= (x^2 - \frac{4}{9})(x^2 + \frac{4}{9})(x^4 + \frac{16}{81}) } $$

$$ \hspace*{10 mm}\mathrm{= (x - \frac{2}{3})(x + \frac{2}{3})(x^2 + \frac{4}{9})(x^4 + \frac{16}{81}) } $$