(i) 32² = (30 + 2)²

= 30 (30 + 2) + 2 (30 + 2)

= 30² + 30 x 2 + 2 x 30 + 2²

= 900 + 60 + 60 + 4

= 1024

(ii) The number 35 has 5 in its unit's place. Therefore,

35² = (3) (3 + 1) hundreds + 25

= (3 x 4) hundreds + 25

= 1200 + 25 = 1225

(iii) 86² = (80 + 6)²

= 80 (80 + 6) + 6 (80 + 6)

= 80² + 80 x 6 + 6 x 80 + 6²

= 6400 + 480 + 480 + 36

= 7396

(iv) 93² = (90 + 3)²

= 90 (90 + 3) + 3 (90 + 3)

= 90² + 90 x 3 + 3 x 90 + 3²

= 8100 + 270 + 270 + 9

= 8649

(v) 71² = (70 + 1)²

= 70 (70 + 1) + 1 (70 + 1)

= 70² + 70 x 1 + 1 x 70 + 1²

= 4900 + 70 + 70 + 1

= 5041

(vi) 46² = (40 + 6)²

= 40 (40 + 6) + 6 (40 + 6)

= 40² + 40 x 6 + 6 x 40 + 6²

= 1600 + 240 + 240 + 36

= 2116