Simplify the following using the identities:(i) \(\frac{58^2-42^2}{16

1.	Simplify the following using the identities:(i) \(\frac{58^2-42^2}{16}\)(ii) 178 x 178 - 22 x 22(iii) \(\frac{198\times 198-102\times 102}{96}\)(iv) 1.73 x 1.73 - 0.27 x 0.27(v) \(\frac{8.63\times 8.63-1.37\times 1.37}{0.726}\)
Answer» (i) \(\frac{58^2-42^2}{16}\) = \(\frac{(58-42)(58-42)}{4\times 4}\) = \(\frac{16(100)}{16}\) = 100 (ii) 178 x 178 - 22 x 22 (178)² – (22)² = (178 + 22) (178 – 22) = 200 × 156 = 31200 (iii) \(\frac{198\times 198-102\times 102}{96}\) = \(\frac{(198-102)(198+102)}{96}\) = \(\frac{96\times 300}{96}\) = 300 (iv) 1.73 x 1.73 - 0.27 x 0.27 (1.73) – (0.27) = (1.73 + 0.27) (1.73 – 0.27) = 2 (1.46) = 2.92 (v) \(\frac{8.63\times 8.63-1.37\times 1.37}{0.726}\) = \(\frac{(8.63+1.37)(8.63-1.37)}{0.726}\) = \(\frac{10\times 7.26}{0.726}\) = 100

Simplify the following using the identities:(i) \(\frac{58^2-42^2}{16}\)(ii) 178 x 178 - 22 x 22(iii) \(\frac{198\times 198-102\times 102}{96}\)(iv) 1.73 x 1.73 - 0.27 x 0.27(v) \(\frac{8.63\times 8.63-1.37\times 1.37}{0.726}\)

Answer»

(i) \(\frac{58^2-42^2}{16}\)

= \(\frac{(58-42)(58-42)}{4\times 4}\)

= \(\frac{16(100)}{16}\)

= 100

(ii) 178 x 178 - 22 x 22

(178)² – (22)²

= (178 + 22) (178 – 22)

= 200 × 156

= 31200

(iii) \(\frac{198\times 198-102\times 102}{96}\)

= \(\frac{(198-102)(198+102)}{96}\)

= \(\frac{96\times 300}{96}\)

= 300

(iv) 1.73 x 1.73 - 0.27 x 0.27

(1.73) – (0.27)

= (1.73 + 0.27) (1.73 – 0.27)

= 2 (1.46)

= 2.92

(v) \(\frac{8.63\times 8.63-1.37\times 1.37}{0.726}\)

= \(\frac{(8.63+1.37)(8.63-1.37)}{0.726}\)

= \(\frac{10\times 7.26}{0.726}\)

= 100