Select and use the identity that will help you to find the following products without multiplying directly: Class 9

Select and use the identity that will help you to find the following products without multiplying directly: Class 9

Question 1.

Select and use the identity that will help you to find the following products without multiplying directly: Class 9

i. (41)²

ii. (27)²

iii. (23 × 17)

iv. (135)²

V. (97)²

vi. (18 × 29)

vii. (34 × 43)

viii. (205)²

Solution:

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

(41 )² = (40 + 1)²

= 40² + 2(40)(1) + 1²

= 1600 + 80 + 1 = 1681

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

(27)² = (30 - 3)²

= 30² - 2(30)(3) + 3²

= 900 - 180 + 9 = 729

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

(23 × 17) = (20 + 3)(20 - 3)

= 20² - 3²

= 400 - 9

= 391

iv. Using Shridharacharya identity:

a² = (a + b)(a - b) + b²

(135)² = (135 + 5)(135 - 5) + 5²

= (140)(130) + 25

= 18200 + 25

= 18225

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

(97)² = (100 - 3)²

= 100² - 2(100)(3) + 3²

= 10000 - 600 + 9

= 9409

vi. Using identity: (x + a)(x + b) = x² + (a + b)x + ab

(18 × 29) = (23 - 5)(23 + 6)

= 23² + (- 5 + 6)(23) + (- 5)(6)

= 529 + 23 - 30 = 522

vii. Using identity: (x + a)(x + b) = x² + (a + b)x + ab

(34 x 43) = (30 + 4)(30 + 13)

= 30² + 30(4 + 13) + (4)(13)

= 900 + 30(17) + 52

= 900 + 510 + 52

= 1462

viii. Using Shridharacharya identity:

a² = (a + b)(a -b) + b²

(205)² = (205 + 5)(205 - 5) + 5²

= (210)(200) + 25

= 42000 + 25

= 42025