Find the following squares using one of the above identities. Determine which of these identities Class 9

Find the following squares using one of the above identities. Determine which of these identities Class 9

Question 1.

Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. Class 9

i. 117²

ii. 78²

iii. 198²

iv. 214²

v. 1104²

vi. 1120²

Solution:

i. Using identity: (a + b)² = a² + 2ab + b²

117² = (100 +17)²

= 100² + 2(100)(17) + 17²

= 10000 + 3400 + 289

= 13689

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

78² = (80 - 2)²

= 80² - 2(80)(2) + 2²

= 6400 - 320 + 4

= 6084

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

198²= (200 - 2)²

= 200² - 2(200)(2) + 2²

= 40000 - 800 + 4 = 39204

iv. Using identity: (a + b)² = a² + 2ab + b²

214² = (200 + 14)²

= 200² + 2(200)(14) + 14²

= 40000 + 5600 + 196 = 45796

v. Using identity: (a + b)² = a² + 2ab + b²

1104² = (1100 + 4)² = 1100² + 2(1100)(4) + 4²

= 1210000 + 8800 + 16

=1218816

vi. Using identity: (a + b)² = a² + 2ab + b²

1120² = (1100 + 20)² = 1100² + 2(1100)(20) + 20²

= 1210000 + 44000 + 400

=1254400