Simplify each of the following :

(i) $175\times 175+2\times 175\times 25+25\times 25$

(ii) $322\times 322-2\times 322\times 22+22\times 22$

(iii) $0.76\times 0.76+2\times 0.76\times 0.24+0.24\times 0.24$

(iv) $\frac{7.83\times 7.83-1.17\times 1.17}{6.66}$

$\left(i\right)175\times 175+2\times 175\times 25+25\times 25\text{Let}a=175\text{and}b=25,\text{then}{a}^2+2ab+b^2=(a+b{)}^2=(175+25{)}^2=(200{)}^2=40000(ii)322\times 322-2\times 322\times 22+22\times 22\text{Let}a=322\text{and}b=22,\text{then}{a}^2-2ab+b^2=(a-b{)}^2=(322-22{)}^2=(300{)}^2=90000\left(iii\right)0.76\times 0.76+2\times 0.76\times 0.24+0.24\times 0.24\text{Let}a=0.76\text{and}b=0.24,\text{then}{a}^2+2ab+b^2=(a+b{)}^2=(0.76+0.24{)}^2=(1.00{)}^2=1(iv)\frac{7.83\times 7.83-1.17\times 1.17}{6.66}\text{Let}a=7.83,b=1.17,a-b=7.83-1.17=6.66\frac{a\times a-b\times b}{a-b}=\frac{a^2-b^2}{a-b}=\frac{(a+b)(a-b)}{a-b}=a+b=7.83+1.17=9.00=9$