Question

Solve this question​

Answer 1

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${}{ \tt{ \green{identity \: used - }}}$

$1. \: (a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab \\ 2. \: (a - b) {}^{2} = {a}^{2} + {b}^{2} - 2ab \\ 3. \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

${}{ \huge{{ \purple{hope \: it \: helps \: you...}}}}$

Answer 2

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❖ ANSWER ❖

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1) 71² =(70 +1)²

Using identity ( a+ b)² = a² +2ab +b²

71 ² =70² +140 +1

= 4900 +140 +1

= 5041

2) 99² =(100 - 1)²

Using identity ( a- b)² = a² - 2ab +b²

100² - 2(100)(1) +1²

10000 - 200 +1 =9801

3) 102² =( 100+2 )²

Using identity ( a+ b)² = a² +2ab +b²

100² +2(100)(2) +2²

1000 +400 +4 =10404

4) 998 =(1000 - 2)²

Using identity ( a- b)² = a² - 2ab +b²

1000² - 2(1000)(2) +2²

=996004

5)( 5.2)² = (5 +0.2) ²

Using identity ( a+ b)² = a² +2ab +b²

(5 +0.2) ²= 5² +2(5)(0.2) +0.2²

= 27.04

6) 297 ×303

= (300 - 3)(300 +3)

Using identity a²-b²=(a-b)(a +b)

(300 - 3)(300 +3)= 300² - 3²

= 90000 - 9

= 89991

(7) 78 ×82 =(80-2)(80 +2)

Using identity a²-b²=(a-b)(a +b)

(80-2)(80 +2)=80²-2²

= 6400 - 4

= 6396

(8)(8.9)² =(9 - 0.1)²

Using identity ( a- b)² = a² - 2ab +b²

(9 - 0.1)² =9² - 2(9)(0.1) +0.1²

= 79.21

(9) 10.5×9.5 =(10 +0.5)(10 - 0.5)

Using identity a²-b²=(a-b)(a +b)

(10 +0.5)(10 - 0.5) =10² - 0.5²

= 100 - 0.25

= 99.75

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I hope it may help you

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