Find 406², 72², 145², 1097², and 124² using the identities you have learnt so far. Class 8

Find 406², 72², 145², 1097², and 124² using the identities you have learnt so far. Class 8

Question 1.

Find 406², 72², 145², 1097², and 124² using the identities you have learnt so far. Class 8

Solution:

406² = (400 + 6)²

= 400² + 2 × 400 × 6 + 6²

= 160000 + 4800 + 36 = 164836 722

72² = (70 + 2)² = 70² + 2 × 70 × 2 + 2²

= 4900 + 280 + 4 = 5184

145² = (150 - 5)²

= 150² - 2 × 150 × 5 + 5²

= 22500 - 1500 + 25 = 21025.

1097² = (1100 - 3)²

= 1100² - 2 × 1100 × 3+ 3²

= 1210000 - 6600 + 9 = 1203409

124² = (100 + 24)²

= 100² + 2 × 100 × 24 + 24²

= 10000 + 4800 + 576 = 15376

Question 2.

Do Patterns 1 and 2 hold only for counting numbers? Do they hold for negative integers as well? What about fractions? Justify your answer. Class 8

Solution:

Yes, because it has been shown that they are true of any two unknown numbers a and b.