1
Question
Find the values of the following:
(1) 422
(2) 1052
(3) 512
(4) 1022
(5) 532
(1) 422
(2) 1052
(3) 512
(4) 1022
(5) 532
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Solution
(1) 422
42 = 40 + 2
∴ 422 = (40 + 2)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 422 = (40 + 2)2
= (40)2 + 2 (40) (2) + (2)2
= 1600 + 160 + 4
= 1764
(2) 1052
105 = 100 + 5
∴ 1052 = (100 + 5)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 1052 = (100 + 5)2
= (100)2 + 2 (100) (5) + (5)2
= 10000 + 1000 + 25
= 11025
(3) 512
51 = 50 + 1
∴ 512 = (50 + 1)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 512 = (50 + 1)2
= (50)2 + 2 (50) (1) + (1)2
= 2500 + 100 + 1
= 2601
(4) 1022
102 = 100 + 2
∴ 1022 = (100 + 2)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 1022 = (100 + 2)2
= (100)2 + 2 (100) (2) + (2)2
= 10000 + 400 + 4
= 10404
(5) 532
53 = 50 + 3
∴ 532 = (50 + 3)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 532 = (50 + 3)2
= (50)2 + 2 (50) (3) + (3)2
= 2500 + 300 + 9
= 2809
42 = 40 + 2
∴ 422 = (40 + 2)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 422 = (40 + 2)2
= (40)2 + 2 (40) (2) + (2)2
= 1600 + 160 + 4
= 1764
(2) 1052
105 = 100 + 5
∴ 1052 = (100 + 5)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 1052 = (100 + 5)2
= (100)2 + 2 (100) (5) + (5)2
= 10000 + 1000 + 25
= 11025
(3) 512
51 = 50 + 1
∴ 512 = (50 + 1)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 512 = (50 + 1)2
= (50)2 + 2 (50) (1) + (1)2
= 2500 + 100 + 1
= 2601
(4) 1022
102 = 100 + 2
∴ 1022 = (100 + 2)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 1022 = (100 + 2)2
= (100)2 + 2 (100) (2) + (2)2
= 10000 + 400 + 4
= 10404
(5) 532
53 = 50 + 3
∴ 532 = (50 + 3)2
Thus, we can use the identity (a + b)2 = a2 + 2ab + b2 .
∴ 532 = (50 + 3)2
= (50)2 + 2 (50) (3) + (3)2
= 2500 + 300 + 9
= 2809
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